Question

In 2017, there were 26,697 restaurants in all of New York City. If restaurants increase in the city at a rate of 2% per year, how many restaurants will there be in New York City In 2023?

Answer 1

We are given that the number of restaurants increases exponentially at a rate of 2%. We will use the following formula for exponential growth:

$P=P_0(1+r)^t$

Where P is the number of restaurants at a time "t", P0 is the initial number of restaurants, "r" is the growth rate in decimal form, and "t" is time. Replacing the values we get:

$P=26697(1+0.02)^t$

Simplifying:

$P=26697(1.02)^t$

Now we replace time t = 6, since there are 6 years between 2017 and 2023:

$P=26697(1.02)^6$

Solving the operations:

$P=30065.2$