Given the Exponential Function, determine the Initial Value and Rate of Change as a Percent for each of the following.

Question

Find Initial Value, Growth/Decay Rate as a %

 

h(x)=4133(1.085)^x

 

f(x)=3680(0.71)^x

 

g(x)=1490(1.06)^x

 

f(x)=256(1.25)^x

 

p(t)=715(1.07)^t

 

d(t)=(0.91)^t

Answer 1

In an exponential function,

 

A = P(1 + r)^t

 

P = initial value

r = growth rate

 

 

In this case for the first one, r=0.085

 

Therefore, the growth rate is 8.5%

Answer 2

The initial value is found by pluggin in 0.

e.g for the first one 

h(0) = 4133(1.085)⁰ = 4133. Any number raised to 0 is 1.

 

the growth rate is 1.085 which is 108.5% (move decimal 2 over to get percent)

 

in each example the number in front of the parenthesis is the initial rate (if there is no number then initial rate is 1)

the number in parenthesis is the growth/decay rate. If the number is > 1 it is a growth rate. If it is < 1 it is the decay rate.

best - david