Question

A populations instantaneous growth rate is the rate at which it grows for every instant in time. Function r gives the instantaneous growth rate of a bacterial culture x hours after the start of an experiment How many hours after the experiment began was the instantaneous growth rate equal to 0? r(x)=0.01(x+2)(x^2 -9) A. 9 B. 2 C. 0 D. 3

Answer 1

Answer:

3

Step-by-step explanation:

r(x) = 0.01(x + 2)(x^2 - 9)

We are looking fo the value of x at which r(x) = 0.

We set the function equal to 0 and solve for x.

0.01(x + 2)(x^2 - 9) = 0

Divide both sides by 0.01. Factor x^2 - 9 as the difference of two squares.

(x + 2)(x + 3)(x - 3) = 0

x + 2 = 0  or  x + 3 = 0  or x - 3 = 0

x = -2  or x = -3  or x = 3

Since we are looking for a time after the experiment started, and it started at x = 0, we discard the negative answers, and we keep x = 3.

Answer: 3