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There are $170$ deer on a reservation. The deer population is increasing at a rate of $30\%$ per year. Write a function that gives the deer population $p(t)$ on the reservation $t$ years from now.

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Write exponential functions: word problems

Full solution

Q. There are

170

deer on a reservation. The deer population is increasing at a rate of

30\%

per year. Write a function that gives the deer population

p(t)

on the reservation

t

years from now.

Identify Initial Population and Growth Rate: First, let's identify the initial population $a$ and the growth rate $r$ . $\newline$ Initial population $a$ : $170$ deer $\newline$ Growth rate $r$ : $30\%$ per year, which can be written as a decimal $0.30$
Determine Growth Factor: Next, we need to determine the growth factor $b$ . The growth factor is calculated by adding $1$ to the growth rate expressed as a decimal. $\newline$ Growth factor $b$ = $1 + r$ $\newline$ Let's calculate the value of $b$ . $\newline$ $b = 1 + 0.30$ $\newline$ $b = 1.30$
Write Exponential Function: Now we can write the exponential function that models the deer population $p(t)$ after $t$ years. $\newline$ The general form of an exponential growth function is $p(t) = a(b)^t$ . $\newline$ Substitute $170$ for ' $a$ ' and $1.30$ for ' $b$ ' to get the specific function for this problem. $\newline$ $p(t) = 170(1.30)^t$

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