{{asɛmtiNe Ɔkyerɛwfo}} | Nhomakorabea | Nneɛma a ɛma wotumi yɛ ade

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1

Simplify (-3x^{-1}y^{2}z)^{3}(-2x^{0}y^{-5}z^{-1})

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Simplify \frac{72x^{-9}y^{-3}z}{16x^{3}y^{-3}z^{-6}}

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1

Condense the following expression into a single expression:
\frac{1}{2}\log_{3}x - 4 log_{3}y

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1

Condense the following expression into a single expression:
3lnx+\frac{1}{3}lny-ln2

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1

Expand the following expression:
lnx^{2}y^{4}z

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1

Expand the following expression:
\frac{log_{4}a^{3}\sqrt[3]{c}}{log_{4}b^{2}}

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1

Solve 4\cdot5^{2x+1}=500

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1

Solve 7^{3x+1}=49^{x+1}

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1

Solve 3\cdot6^{x-8}=648

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1

Solve 9^{2x+1}=81^{3x+4}

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1

Solve log_{3}(4x+773)=6

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1

Solve 5+log_{4}(2x+63)=8

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1

Solve log_{5}(6x-19)=3

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Solve log_{3}(10x-9)+6=10

Consider the function f(x)=p(0.5)^{x}+q, where p and q are constants. The graph of f(x) passes through the points (0,6) and (1,4).

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Write down an equation relating p and q.

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Write down the other equation relating p and q.

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Find the value of p and q.
Type your answer in p=,q=
No Spaces

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Write down the equation of the horizontal asymptote to the graph of f(x).

The pH of a solution measures its acidity and can be determined using the formula pH=-log_{10}C, where Cis the concentration of hydronium ions in the solution, measured in moles per liter. A lower pH indicates a more acidic solution.

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The concentration of hydronium ions in a particular type of coffee is 1.30\cdot10^{-5} moles per liter. Calculate the pH of the coffee.

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A different, unknown, liquid has 10 times the concentration of hydronium ions of the coffee in part (a). Determine whether the unknown liquid is more or less acidic than the coffee. Justify your answer mathematically.

The population of mosquitoes decreases exponentially. The size of the population, P, after t days is modeled by the equation P=3200\cdot2^{-t}+50 where t\geq0.

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Write down the exact size of the initial population.

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Find the size of the population after 4 days.

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Calculate the time it will take for the size of the population to decrease to 60.

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The population will stabilize when it reaches a size of k. Write down the value of k.

Little Green island originally had no turtles. After 55 turtles were introduced to the island, their population is modeled by N(t)=a\cdot2^{-t}+10, t\geq0,where a is a constant and t is the time in years since the turtles were introduced.

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1

Find the value of a.

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Find the time, in years, for the population to decrease to 20 turtles.

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There is a number m beyond which the turtle population will not decrease. Find the value of m. Justify your answer.

A population of 200 rabbits was introduced to an island. One week later the number of rabbits was 210. The number of rabbits, N , can be modeled by the function N(t)=200×b^{t}, t\geq0 , where t is the time, in weeks, since the rabbits were introduced to the island.

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Find the value of b.

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Calculate the number of rabbits on the island after 10 weeks.

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An ecologist estimates that the island has enough food to support a maximum population of 1000 rabbits. Calculate the number of weeks it takes for the rabbit population to reach this maximum.

Sejah placed a baking tin, that contained cake mix, in a preheated oven in order to bake a cake. The temperature in the center of the cake mix, T, in degrees Celsius (°C) is given by T(t)=150-a(1.1)^{-t}, where t is the time, in minutes, since the baking tin was placed in the oven. The temperature in the centre of the cake mix was 18 °C when placed in the oven.

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1

Find the value of a.

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The baking tin is removed from the oven 15 minutes after the temperature in the center of the cake mix has reached 130 °C. Find the total time that the baking tin is in the oven.
Hint GDC!

The growing population of cats in my gnome garden forced the gnomes to migrate to my attic, so now the population of gnomes in my attic grows according to the logistic model P(t)=\frac{110}{1+27.3e^{-0.14t}}, where t is measured in days.

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How many gnomes can my attic support?

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What is the initial population of gnomes in my attic?

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How many gnomes are present after a fortnight?

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When will there be 72 gnomes in my attic?

Data for a small city’s population is shown below. P(t)=\frac{500,000}{1+9e^{-0.125t}}, t\geq0 where t is the number of years since 1980.

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What was the population of the city in 1980?

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What was the population of the island in 2000?

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Assuming that this model will also be valid in the future, what is the largest population that will ever be on the island?

A cup of boiling water is placed in a room to cool. The temperature of the room is 20°C . This situation can be modelled by the exponential function T=a+b(k^{-m}), where T is the temperature of the water, in °C , and m is the number of minutes for which the cup has been placed in the room. A sketch of the situation is given as follows.

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0

Explain why a=20.

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Initially, at m=0, the temperature of the water is 100°C. Find the value of b.

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0

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0

Solve log_{2}(x+3)+log_{2}(x-3)=4

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Unit 5 Study Guide

Unit 5 Study Guide

Simplify (-3x^{-1}y^{2}z)^{3}(-2x^{0}y^{-5}z^{-1})

Simplify \frac{72x^{-9}y^{-3}z}{16x^{3}y^{-3}z^{-6}}

Condense the following expression into a single expression:\frac{1}{2}\log_{3}x - 4 log_{3}y

Condense the following expression into a single expression:3lnx+\frac{1}{3}lny-ln2

Expand the following expression:lnx^{2}y^{4}z

Expand the following expression:\frac{log_{4}a^{3}\sqrt[3]{c}}{log_{4}b^{2}}

Solve 4\cdot5^{2x+1}=500

Solve 7^{3x+1}=49^{x+1}

Solve 3\cdot6^{x-8}=648

Solve 9^{2x+1}=81^{3x+4}

Solve log_{3}(4x+773)=6

Solve 5+log_{4}(2x+63)=8

Solve log_{5}(6x-19)=3

Solve log_{3}(10x-9)+6=10

Write down an equation relating p and q.

Write down the other equation relating p and q.

Find the value of p and q.Type your answer in p=,q=No Spaces

Write down the equation of the horizontal asymptote to the graph of f(x).

The concentration of hydronium ions in a particular type of coffee is 1.30\cdot10^{-5} moles per liter. Calculate the pH of the coffee.

A different, unknown, liquid has 10 times the concentration of hydronium ions of the coffee in part (a). Determine whether the unknown liquid is more or less acidic than the coffee. Justify your answer mathematically.

Write down the exact size of the initial population.

Find the size of the population after 4 days.

Calculate the time it will take for the size of the population to decrease to 60.

The population will stabilize when it reaches a size of k. Write down the value of k.

Find the value of a.

Find the time, in years, for the population to decrease to 20 turtles.

There is a number m beyond which the turtle population will not decrease. Find the value of m. Justify your answer.

Find the value of b.

Calculate the number of rabbits on the island after 10 weeks.

An ecologist estimates that the island has enough food to support a maximum population of 1000 rabbits. Calculate the number of weeks it takes for the rabbit population to reach this maximum.

Find the value of a.

The baking tin is removed from the oven 15 minutes after the temperature in the center of the cake mix has reached 130 °C. Find the total time that the baking tin is in the oven. Hint GDC!

How many gnomes can my attic support?

What is the initial population of gnomes in my attic?

How many gnomes are present after a fortnight?

When will there be 72 gnomes in my attic?

What was the population of the city in 1980?

What was the population of the island in 2000?

Assuming that this model will also be valid in the future, what is the largest population that will ever be on the island?

Explain why a=20.

Initially, at m=0, the temperature of the water is 100°C. Find the value of b.

Solve log_{2}(x+3)+log_{2}(x-3)=4

The first three terms of a geometric sequence are lnx^{1}6,lnx^{8},lnx^{4}, for x>0. Find the common ratio.

Simplify (-3x^{-1}y^{2}z)^{3}(-2x^{0}y^{-5}z^{-1})

Simplify \frac{72x^{-9}y^{-3}z}{16x^{3}y^{-3}z^{-6}}

Condense the following expression into a single expression:\frac{1}{2}\log_{3}x - 4 log_{3}y

Condense the following expression into a single expression:3lnx+\frac{1}{3}lny-ln2

Expand the following expression:lnx^{2}y^{4}z

Expand the following expression:\frac{log_{4}a^{3}\sqrt[3]{c}}{log_{4}b^{2}}

Solve 4\cdot5^{2x+1}=500

Solve 7^{3x+1}=49^{x+1}

Solve 3\cdot6^{x-8}=648

Solve 9^{2x+1}=81^{3x+4}

Solve log_{3}(4x+773)=6

Solve 5+log_{4}(2x+63)=8

Solve log_{5}(6x-19)=3

Solve log_{3}(10x-9)+6=10

Write down an equation relating p and q.

Write down the other equation relating p and q.

Find the value of p and q.Type your answer in p=,q=No Spaces

Write down the equation of the horizontal asymptote to the graph of f(x).

The concentration of hydronium ions in a particular type of coffee is 1.30\cdot10^{-5} moles per liter. Calculate the pH of the coffee.

A different, unknown, liquid has 10 times the concentration of hydronium ions of the coffee in part (a). Determine whether the unknown liquid is more or less acidic than the coffee. Justify your answer mathematically.

Write down the exact size of the initial population.

Find the size of the population after 4 days.

Calculate the time it will take for the size of the population to decrease to 60.

The population will stabilize when it reaches a size of k. Write down the value of k.

Find the value of a.

Find the time, in years, for the population to decrease to 20 turtles.

There is a number m beyond which the turtle population will not decrease. Find the value of m. Justify your answer.

Find the value of b.

Calculate the number of rabbits on the island after 10 weeks.

An ecologist estimates that the island has enough food to support a maximum population of 1000 rabbits. Calculate the number of weeks it takes for the rabbit population to reach this maximum.

Find the value of a.

The baking tin is removed from the oven 15 minutes after the temperature in the center of the cake mix has reached 130 °C. Find the total time that the baking tin is in the oven. Hint GDC!

How many gnomes can my attic support?

What is the initial population of gnomes in my attic?

How many gnomes are present after a fortnight?

Condense the following expression into a single expression:
\frac{1}{2}\log_{3}x - 4 log_{3}y

Condense the following expression into a single expression:
3lnx+\frac{1}{3}lny-ln2

Expand the following expression:
lnx^{2}y^{4}z

Expand the following expression:
\frac{log_{4}a^{3}\sqrt[3]{c}}{log_{4}b^{2}}

Find the value of p and q.
Type your answer in p=,q=
No Spaces

The baking tin is removed from the oven 15 minutes after the temperature in the center of the cake mix has reached 130 °C. Find the total time that the baking tin is in the oven.
Hint GDC!

Condense the following expression into a single expression:
\frac{1}{2}\log_{3}x - 4 log_{3}y

Condense the following expression into a single expression:
3lnx+\frac{1}{3}lny-ln2

Expand the following expression:
lnx^{2}y^{4}z

Expand the following expression:
\frac{log_{4}a^{3}\sqrt[3]{c}}{log_{4}b^{2}}

Find the value of p and q.
Type your answer in p=,q=
No Spaces

The baking tin is removed from the oven 15 minutes after the temperature in the center of the cake mix has reached 130 °C. Find the total time that the baking tin is in the oven.
Hint GDC!