differential equations: slope fields, separation of variables and exponential models

Review differential equations: slope fields, separation of variables and exponential models for AP Calculus AB and try 1 free AP-style practice question. 24 questions on this topic in AP Calculus AB · Unit 7 · Differential Equations.

Try a free question

Question 1

A colony of bacteria satisfies $\frac{dP}{dt} = kP$ , where $P(t)$ is measured in bacteria and $t$ in hours. If $P(0) = 45$ and $P'(0) = 18$ , what is $P(14)$ ?

23 more questions on this topic

Full practice for AP Calculus AB · Unit 7 · Differential Equations: timed tests, step-by-step explanations for every answer, and AI grading for free-response questions.

Start practicing free

Inside the course

How practice works on S&D Academy

Answer, then see why

The price of gasoline rises 10% and the quantity demanded falls 5%. What happens to total revenue?

Not quite. The answer is B.

Why the other options are wrong

AI grading for free-response

Write your FRQ answer and get it scored point by point against the AP rubric, with the line from your answer that earned or missed each point.

Question 13 / 4 pts

Part a1 / 1 pts

Point 1: Earned

94% sure

Reason: Correctly identifies demand for gasoline as inelastic.

Evidence: "The price of gasoline rises and the quantity falls only a little."

Part b2 / 3 pts

Point 1: Earned

91% sure

Reason: Graph shows relatively inelastic demand.

Evidence: Draws a steep demand curve.

Point 2: Earned

88% sure

Reason: Correct new equilibrium price.

Evidence: Shifts supply left, P1 → P2.

Point 3: Not earned

82% sure

Reason: With inelastic demand, a price increase raises total revenue.

Evidence: "Revenue goes down."

Differential equations: slope fields, separation of variables and exponential models: AP Calculus AB Practice Questions | S&D Academy