exponential functions

Question

In
2003
, a city had a population of
360,000
people. Each year since, the population has grown by
9.3%
.
Let
t
be the number of years since
2003
. Let
y
be the city's population.
Write an exponential function showing the relationship between
y
and
t
.

Answer 1

Hi Latosha,

 

The tricky part of this equation is the rate at which the population grows.  If it grows by 9.3% each year, then the growth factor is 100% + 9.3% which is 109.3% which as a decimal is written as 1.093.

 

So, the function that gives the population is

 

y = 360,000(1.093)^t

 

Hope this helps!  :)

 

Answer 2

y = 360000(1 + 0.093)^t

 

y = 360000(1.093)^t