Question

A city's population is currently 189,000. If the population doubles every 55 years, what willthe population be 275 years from now?

Answer 1

`6,048,000`

Step-by-step explanation

The population doubles every 55 years. This implies that the rate of increase is 200% or 2 times and the time will be measured in terms of 55 years.

We can write an exponential function representing this:

`A=A_0\cdot r^{(t)/(55)}`

where t = number of years

r = rate = 2

A0 = initial population of city

We have to solve for A when t = 275.

Therefore:

`\begin{gathered} A=189000\cdot2^{((275)/(55))} \\ A=189000\cdot2^5 \\ A=6,048,000 \end{gathered}`

That will be the population 275 years from now.