AP Calculus AB 7.8 Exponential Models with Differential Equations Questions

Model exponential growth and decay with differential equations, interpret proportional rates and solve for particular functions in context.

Exam points

separate variables and integrate both sides of a differential equation
apply an initial or particular condition to determine the constant

Covered syllabus points

FUN-7.F—Interpret the meaning of a differential equation and its variables in context FUN-7.G—Determine general and particular solutions for problems involving differential equations in context

[Maximum number: 1]

A population described by a function P at time t decreases at a rate proportional to P. Which of the following differential equations could describe the rate of change of the population?

$\frac{d P}{d t}=-0.015 P$

$\frac{d P}{d t}=-\frac{0.015}{P}$

$\frac{d P}{d t}=-0.02 t$

$\frac{d P}{d t}=6 e^{-0.02 t}$

[Maximum number: 1]

If $f^{\prime}(x)=2 f(x)$ and f(2)=1, then f(x)=

$e^{2 x-4}$

$e^{2 x}+1-e^{4}$

$e^{4-2 x}$

$e^{x^{2}-4}$

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Covered syllabus points

Question 1

Question 2