Question

Consider this function for cell duplication where the cells duplicate every minute.

f(x) = 75(2)x
Determine what each parameter in the function represents.
A) The 75 is the initial number of cells, and the 2 indicates that the number of cells doubles every minute.
B) The 75 is the initial number of cells, and the 2 indicates that the number of cells increases by 2 every minute.
C) The 75 is the number of cells at 1 minute, and the 2 indicates that the number of cells doubles every minute.
D) The 75 is the number of cells at 1 minute, and the 2 indicates that the number of cells increases by 2 every minute.

Answer 1

A) The 75 is the initial number of cells, and the 2 indicates that the number of cells doubles every minute.

Explanation:

The function for cell duplication where the cells duplicate every minute, is given by
`f(x)=75(2)^x`

The initial number of cells occurs when x=0:

`f(0)=75(2)^0`

Note that every non-zero number to the exponent of zero is 1.

`\implies f(0)=75(1)=75`Therefore the initial number of cells is 75

The two is the multiplicative rate of change, therefore the 2 indicates that the number of cells doubles every minute.