hi..derivative question.....plizzz help...thnx (hav the answer)?

Question

find a formula for the change in populaetion (P't)
if P(t) is

p(t) = 40(3/2)^t/3

thanx!!!

the answer is:
P'(t) = 40/3 * ln3/2 * (3/2)^t/3

tnanx!!!

iv stated the question and have the answer, dont know how to get it

Answer 1

d/dx(a^x) = lna * a^x

Applying the formula your answer comes directly

Answer 2

1. You can put the constant (40) outside of the derivative and just multiply the result by it.

2. The derivative of a^x is a^x * ln a

3. The derivative of a^f(x) is a^f(x) * ln a * the derivative of f(x).
(In your case, f(x) is t/3, and its derivative is 1/3

So, for p(t) = 40(3/2)^t/3

The derivative with respect to t is:

40 [(3/2)^t/3 * ln 3/2 * 1/3]

I hope this helps you see the process.

Answer 3

S(hi)=75/70*integer 8/9^tt
so using this formulae population =shitt

Answer 4

What is your question?