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AP Calculus AB 7.8 Exponential Model Solutions

Find exponential growth or decay solutions from a proportional-rate differential equation and determine constants from initial conditions.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

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

FUN-7.G—Determine general and particular solutions for problems involving differential equations in context question 1

[Maximum number: 1]

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

A

e2x−4e^{2 x-4}

B

e2x+1−e4e^{2 x}+1-e^{4}

C

e4−2xe^{4-2 x}

D

ex2−4e^{x^{2}-4}

All question bank results loaded