Question

What exponential function represents the data in the table?

x f(x)
3 64
4 256
5 1024

Answer 1

Answer:
`f(x)=4^x`

Explanation:

The general exponential function is given by :-

`f(x)=Ab^x`, where A is initial amount , b is multiplicative growth rate and x is time period.

Also, the multiplicative growth rate is the common ratio of the consecutive terms.

From the given table ,
`b=(256)/(64)=4`

Substitute, x = 3 , f(x)=64 and b=4 , we get

`64=A(4)^3\\\\\Rightarrow\ 64=A(64)\\\\\Rightarrow\ A=1`

Hence, the exponential function represents the data in the table is

`f(x)=(1)(4)^x\\\\\Rightarrow\ f(x)=4^x`