For the exponential function represented in the table below

For the exponential function represented in the table below, determine the initial value the n -unit growth actors, and die exponential function that models the data. a. The initial value: b The 1-unit growth factor: c. The 1-unit percent change: d. The 3-unit growth factor: 8044 e. The 1/4-unit growth factor: f. Function definition:

Solution

function is of form y=a*b^x

a*b¹=756.09

a*b⁴=608.17

b⁴_/b=608.17_/756.09

b³=0.8043619

b=0.93

a*b¹=756.09

a*0.93¹=756.09

a=813

a)initial value =813

b)1 unit growth factor =0.93

c)1 unit percentage chage =(1-0.93)*100% =7%

d)3 unit growth factor =0.93³=0.8044

e)1/4 th unit growth factor =0.93^1/4=0.982

f)function definition : y =813*0.93^x