Question

Find C and a so that ​f(x)equalsCa Superscript x models the situation described. State what the variable x represents in your formula. There are initially 3000 ​bacteria, and this sample doubles in size every hour.

Answer 1

Answer: x represents the time period.

C= 3000 and a = 2

Explanation:

The given equation is
`f(x)=Ca^x` which is an exponential equation. (i)

The general form of the exponential equation is :

`f(x)=Ab^x` (ii)

, where A = initial value and b= multiplicative factor, and x is the time.

As compare both of the equation in (i) and (ii) , we get

A= C , and b= a

Since there are initially 3000 ​bacteria, and this sample doubles in size every hour.

i.e. C= 3000 (Initial) and a= 2 (multiplicative factor).