Question

What exponential function represents the data in the table?

x f(x)
3 64
4 256
5 1024

Answer 1

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

Step-by-step 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 , $b=\dfrac{256}{64}=4$

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

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