Question

In Miami, the number of highway accidents increased by 20% over a four year period. How many accidents were there in 2013 if there were 5,120 in 2009?

Answer 1

We can model this scenario by using the exponential growth formula and plugging in values we know:

$A = P(1+r)^{t}$

A, the resulting amount, is unknown
P, the principle (starting) amount, is 5120
r, the rate at which P increases, is .05 (if a .2 increase spans over 4 years, there is a .05 increase each year)
t, the amount of time that has passed, is 4

The equation now looks like this:

$A = 5120(1.05)^{4}$

To find A, we just need to simplify the other side:

$A = 6223.392$

In 2013, there were ~6224 Miami highway accidents (I rounded up because the amount was more than 6223, and you can't have a fraction of a car accident).

Answer 2

.20 x 5,120 = 1024        1024 + 5120 = 6144