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Quiz 7.2 - Properties, Applications, and Mixed Modelling

Last updated almost 4 years ago
16 questions
5

Match the expressions using the properties of logarithms or exponents.

(Hint: You can try these out in your calculator by setting a, m, and n to different numbers.)

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

Given the following exponential function, identify whether it represents exponential growth or decay, and determine the percentage rate of increase or decrease.

y=420(.981)^{x}

1

Given the following exponential function, identify whether it represents exponential growth or decay, and determine the percentage rate of increase or decrease.

y=800(1.078)^{x}

1

Given the exponential function y=104(.77)^{x}, what is the percentage rate of growth/decay?

Enter your answer as an integer, no "%" or spaces.

1

Given the following exponential function, identify whether it represents exponential growth or decay, and determine the percentage rate of increase or decrease per unit of x.

y=800(2.718)^{0.244x}

1

Given the following exponential function determine the percentage rate of increase or decrease per unit of x.

y=(4)^{-2x}

Enter your answer as a 4-digit number.

1

1

The function f(t) = 9200(0.79)^{t} represents the change in a quantity over t years. What does the constant 0.79 reveal about the rate of change of the quantity?

1

(Hint: find the equivalent monthly rate.)

1

Dan and Ben invested the same amount in savings. Dan earns a certain rate of monthly interest, while Ben earns a certain rate of yearly interest. If they both end the year with the same amount of interest collected, who's interest rate is greater, Dan's or Ben's?

2

Categorize the following situations by the model that best suits them.

  • The amount of gas in a tank after some distance driving.
  • The value of a savings account some time after collecting interest.
  • The path of a rock some time after it is launched from a catapult.
  • The population of rabbits after some time without predation.
  • The total amount of calories consumed after eating some number of M&Ms.
  • Linear
  • Quadratic
  • Exponential Growth
A biologist is studying the growth of a bacterial colony in a petri dish. The table below shows the number of cells in the petri dish after some weeks during the study.



When finding a regression model, the biologist gets the following values for r:
Linear: 0.8233
Quadr: 0.9804
Expon: 0.9905
Logar: 0.6934
1

Based on the r-values, what model best fits this data?

1

What will be the number of cells in week 6?

Round to the nearest whole number.

1

In what week will the number of cells reach one billion (1,000,000,000)?

Enter your answer as a number rounded to the nearest tenth.

The table below lists the time it takes for a turkey to reach certain temperatures after being pulled from a hot oven.



When finding a regression model, a student gets the following values for r:

Linear: 0.9068
Expon: error
Logar: 0.9708
1

According the r-values given, which model best suits the data?

1

Estimate the number of minutes the turkey will take to cool to a temperature of 70.

Enter your answer as a number rounded to the nearest tenth.

Note: it will be in between two of the time values, which is strange. It's okay.