Question

Function f is an exponential function. x −1 1 3 5 7 f(x) 14 4 64 1024 16,234 By what factor does the output value increase as each input value increases by 1? Enter your answer in the box.

Answer 1

Function f is an exponential function.

x      −1     1     3          5           7

f(x)     14    4   64     1024     16,234

We use exponential function y =ab^x

We find out factor b

When x=1 then y=4, so equation becomes $4=ab^1$

When x=3 then y=64, so equation becomes $64=ab^3$

Divide the second equation by first equation

$\frac{64=ab^3}{4=ab^1}$

16 = b^2

Take square root on both sides

So b = +-4

f(x) is increasing, so b= 4

Answer is 4