This math test contains 4 problems with multiple parts each. Problem 1 involves exponential growth modeling with unknown variables C and k. Problem 2 models road clearing using a logarithmic function. Problem 3 involves compound interest calculations for an account that doubles every 7.75 years. Problem 4 analyzes chemical reaction data and fits linear and logarithmic regressions to determine yields at given times.

1. Math 4R Test5A Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(1) Let f(t) = Cekt given f(0) = 0.5 and f(5) = 5.
(1a) Find C
(1b) Find k.
(1c) What is the doubling time?
(1d) Interpolate f(1), f(2), f(4) and extrapolate f(8).
(1e) Solve for t: f(t) = 10
a:TEST5A.4Rt

2. Math 4R Test5A Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(2) The number of miles s of roads cleared of snow each hour a
plow is in use is approximated by the model
h
13 ln  
12
s = 25 – for 2 ≤ h ≤ 15
ln3
where h is the depth of snow in inches.
(2a) Find s(2).
(2b) Find s(15).
(2c) Solve for h: s(h) = 50
(2d) Interpret your results in (2a) – (2c).
(2e) Graph y = s(h).
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3. Math 4R Test5A Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(3) A deposit of $750 is made in a savings account for which the
interest is compounded continuously. The balance doubles in 7.75
years.
(3a) What is the annual percentage rate?
(3b) What is the effective yield?
(3c) Find the balance after 10 years.
(3d) When will the balance be $3,000?
(3e) When will the balance be $10,000?
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4. Math 4R Test5A Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(4) The data in the accompanying table gives the yield y (in
milligrams) of a chemical reaction after t minutes.
t y
1 1.5
2 7.4
3 10.2
4 13.4
5 15.8
6 16.3
7 18.2
8 18.3
(4a) Find the best Linear Regression.
(4b) What is the best Logarithmic Regression?
(4c) Using the best regression (pick Linear or Logarithmic),
find y(10).
(4d) Using the best regression (pick Linear or Logarithmic),
solve for t: y(t) = 20.
(4e) Interpret your results in (5c) – (5d).
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