Question

The population of Fantasy City doubles each month. When will the city be half populated if it will be fully populated in 10 months.

Answer 1

Using an exponential function, it is found that the city will be half populated in 9 months.

The population of Fantasy City doubles each month, hence, after t months, the population is given by:

$P(t) = P(0)2^{t}$

• In which P(0) is the initial population.

Fully populated in 10 months, hence, the full population is:

$P(10) = P(0)2^{10} = 1024P(0)$

Hence, half populated is $P(t) = \frac{1024P(0)}{2} = 512P(0)$, hence:

$P(t) = P(0)2^{t}$

$512P(0) = P(0)2^{t}$

$2^t = 512$

$2^t = 2^9$

$t = 9$

The city will be half populated in 9 months.

To learn more about exponential functions, you can take a look at brainly.com/question/25537936