By what factor does the output value increase as each input value increases by 1

Question

asked Aug 10, 2022 187k views

1 Answer

GaloisGirl · Answer 1 · 2022-08-14T22:13:14+0000

Given:

The table of values of an exponential function.

To find:

The factor by which the output value increase as each input value increases by 1.

Solution:

The general exponential growth function is

f(x)=ab^x ...(i)

where, a is initial value and b is growth factor.

From the given table it is clear that the function passes through (0,3). So, put x=0 and f(x)=3 in (i).

3=ab^0

3=a(1)

3=a

From the given table it is clear that the function passes through (2,12). So, put a=3, x=2 and f(x)=12 in (i).

12=3b^2

Divide both sides by 3.

4=b^2

Taking square root on both sides, we get

$\pm √(4)=b$

$\pm 2=b$

Growth factor cannot be negative. So, b=2.

Therefore, the output value increase by factor 2 as each input value increases by 1.