b Substitute x=10 into the equation found in Part A.
A
a f(x)=120 000(0.97)^x
B
b About 88 491
Practice makes perfect
a We can model the decrease of the population using the exponential decay function.
f(x)= a(1- r)^x
In our case, a represents the initial population and r is the percent of annual decrease. Therefore, a= 120 000 and r= 0.03.
f(x)= 120 000(1- 0.03)^x
⇕
f(x)=120 000(0.97)^x
The function f describes the population of the city after x years.
b To determine what the population will be in 10 years we will use the function found in Part A.
f(x)=120 000(0.97)^x
This function can be used to find the population f(x) after x time period, expressed in years. Since we want to know what the population will be after 10 years, we have to substitute x= 10. Let's do it!
