1.4 Practice Problems

J. Zachary Klingensmith

Problem 1.4.1: The number of fish in a pond is measured by the following exponential equation:

$P(t)=300\times 1.04^t.$

How many fish will be in the pond after 1 year? 5 years? 10 years? 50 years? Is this reasonable?

Answer: 312; 365; 444; 2,132

Problem 1.4.2: Evaluate the following logarithms. Round to two decimal places.

$\log_{2}64$

$\log_{5}125$

$\log_{6}100$

$\log_{4}70$

$\log_{8}200$

Answers: 6; 3; 2.57; 3.07; 2.55

Problem 1.4.3: Solve for $t$ when $y=50$ :

$y=10\times 1.04^t$

Answer: 41.035

Problem 1.4.4: Solve for $t$ when $y=200$ :

$y=20\times 1.08^t$

Answer: 29.919

Problem 1.4.5: Solve for $t$ when $y=80$ :

$y=5\times 1.1^t$

Answer: 29.090

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