Q:

In the exponential growth function y = 235(1.15)^x, what is the 1. growth factor? _____________ 2. percent increase? _____________

Accepted Solution

A:
Growth Factor: 1.15
The y-values multiply by 1.15 every unit you increase x by.
Percentage Increase: 15%
If we are multiplying y-values by 1.15 for every unit of x, we are finding 115% (= 1.15 × 100) of the previous value of y;
100% is equivalent to the previous value, so effectively, we are just adding to the previous value 15% of itself to get the next value.
E.g. If x = 1, then:
y = 235(1.15)¹
= 270.25;
The y-value when x =  2 is just:
270.25 + (15% of 270.25)
= 270.25 + (270.25 × (15/100))
= 270.25 + (40.5375)
= 310.7875
The easier way to write and represent this for any value of x is:
y = 235(1.15)ˣ