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HW5: Applications of Exponential Functions (2-day)

Last updated almost 4 years ago
18 questions
Note from the author:
Watch this video for a comparison of simple and compound interest.
Watch this video and this video for another discussion of different but equivalent forms (such as annual vs. monthly equivalent interest.
Watch this video for a comparison of simple and compound interest.
Watch this video and this video for another discussion of different but equivalent forms (such as annual vs. monthly equivalent interest.
1

Vanessa invested 2500 into an account that earns 3.5% annual interest. Write an exponential function to model the situation.

Use f(t)=... format, with t as your variable, no spaces.

1

Vanessa invested 2500 into an account that earns 3.5% annual interest. Find Vanessa's equivalent monthly interest rate, as a percentage.

Enter your answer as a number rounded to 2 decimal places.

1

The population of a small town was 10800 in 2002 and has decreased at 2.5% each year since then. Write an exponential function to model the situation.

Use f(t)=... format, with t as your variable, with no spaces.

1

The population of a small town was 10800 in 2002 and has decreased at 2.5% each year since then. Estimate the poulation of the town in 2020. Round to the nearest person.

Hint: Be careful what number you plug in to your function.

1

Scott has $1600 in savings that earns 2.4% interest compounded monthly. What will the balance of the account be after 30 years?

Enter your answer as a 6-digit number, no spaces or special symbols.

1

f(x) = 1500(1.08)t

Find the rate of growth / decay, as a percentage. Enter your answer as an integer.

1

f(x) = 18000(.997)t

Find the rate of growth/decay as a percentage. Enter your answer as a 1-digit decimal.

1

Use the properties of exponents and logarithms to match the following.

Draggable itemCorresponding Item
log_{b}(a)
a^{m+n}
(ab)^{n}
a^{m\cdot n}
a^{\frac{m}{n}}
\frac{1}{a^{n}}
a^{-n}
a^{n}b^{n}
(a^{m} )^{n}
\sqrt[n]{a^{m}}
a^{m}\cdot a^{n}
\frac{ln(a)}{ln(b)}
1

What is the significance of Euler's number, e? What situation (that we discussed in class) involves e?

1

If f(x) = e^{x}, what is f^{-1}(x), the inverse?

Enter your answer as an expression, no "=" or spaces.

The temperature of a parked, closed car can reach up to 180oF. Computer chips - used in phones - can only operate at 110oF. Suppose a phone is left in a hot car for a long time, then removed and set in a 73oF classroom. After one minute, it is safe to touch (140oF). How many minutes will it take for the phone to be operable?
1

Find the value of the constant k in Newton's Law of Cooling, assuming t is in minutes.

Round to three decimal places.


1

How many minutes will it take for the phone to be operable?

Enter your answer as a number rounded to 2 decimal places.

Anya has $1000 in an account that earns 2% annual interest. Bea has $1000 in an account that earns 2% annual interest, compounded monthly. At the end of one year, who earns more interest, and how much more?
1

Who earns more interest?

1

What is the difference between the amounts earned?

Give your answer in cents, to the nearest cent. Your answer should be a two digit integer.

1

After 10 years, what will be the difference in amounts earned?

Give your answer in dollars, rounded to the nearest cent. For example, if your answer were $12.867, you would type "12.87"

1

For the given function, find the percentage of growth / decay rate per unit of x. Round to three decimal places where necessary.

f(x) = 22\cdot (1.008)^{2x}

1

For the given function, find the percentage of growth / decay rate per unit of x. Round to three decimal places where necessary.

f(x) = \frac{3}{4}\cdot (0.972)^{-x}

1

For the given function, find the percentage of growth / decay rate per unit of x. Round to three decimal places where necessary.

f(x) = 1.999\cdot (1.28)^{\frac{3}{4}x}