Question

A research study shows that a population of elephants in a locality will double in size every $12$ years. The population at the beginning of $2015$ was estimated to be $50$ elephants. If $P$ represents the population $n$ years after $2015$, then which of the following equations represents the model of the population over time?

• A. $P=12+50n$
• B. $P=50+12n$
• C. $P=50{\left(2\right)}^{12n}$
• D. $P=50(2{)}^{\frac{n}{12}}$

Answer 1

The correct option is D $P=50(2{)}^{\frac{n}{12}}$

Initial population of elephants $=50$

Population will double in size every $12$ years.

Let population at any time after $2015=P$

And $n$ is the number of years after $2015$

So, according to question:

$P=50(2{)}^k$........[where $k=12n$]

So,

$P=50(2{)}^{\frac{n}{12}}$