Question

A quantity Q grows exponentially over time t. At time t=2, Q=16 grams, and at time t=5, Q=128 grams. What is Q at t=3?

How do you solve this?

Answer 1

https://brainly.in/question/8393883?answering=true&answeringSource=feedPersonal%2FquestionPage

Answer 2

Answer:

Q2 = Q0 e^kt   = Q0 e^2k = 16    where Q0 = initial amount

Q5 = Q0 e^5k = 128      amount after 5 sec

Q5 / Q2 = e^5k / e^2k = e^3k = 128 / 16 = 8

Then e^3k = 8

ln 8 = 3 k    so k = ln 8 / 3 = .6931

Now you can solve for Q0

Q2 = 16 = Q0 e^(.6931 * 2) = *  4 Q0     and Q0 = 4

Then after 3 sec    Q = 4 * e(3*.6931) = 8

Check:  Q5 = 4 * e^(.6931 * 5) = 128    as originally specified