AP Calculus AB 7.8 Exponential Models with Differential Equations - MCQs - Exam Style Questions
No-Calc Question
Which of the following is the solution to the differential equation \(\displaystyle \frac{dy}{dx}=0.3y\) with the initial condition \(y(0)=10\)?
(A) \(y=10e^{0.3x}\)
(B) \(y=e^{0.3x}+9\)
(C) \(y=\sqrt{0.6x^{2}+100}\)
(D) \(y=0.15x^{2}+10\)
(B) \(y=e^{0.3x}+9\)
(C) \(y=\sqrt{0.6x^{2}+100}\)
(D) \(y=0.15x^{2}+10\)
▶️ Answer/Explanation
Separate variables: \(\dfrac{dy}{y}=0.3\,dx\).
Integrate: \(\ln|y|=0.3x+C \Rightarrow y=C e^{0.3x}\).
Apply \(y(0)=10\): \(10=C\). Hence \(y=10e^{0.3x}\).
✅ Answer: (A)
Integrate: \(\ln|y|=0.3x+C \Rightarrow y=C e^{0.3x}\).
Apply \(y(0)=10\): \(10=C\). Hence \(y=10e^{0.3x}\).
✅ Answer: (A)