Question

a group of scientists introduced 64 birds into a wildlife sanctuary and tracked the number of birds over time. they noticed that the number of birds grew by 50% each year. how many birds will be in the sanctuary after 6 years? write your answer as a whole number. round to the nearest whole number if necessary.

Explanation:

Step1: Identify the formula for exponential growth

The formula for exponential growth is $A = P(1 + r)^t$, where $P$ is the initial amount, $r$ is the growth rate as a decimal, and $t$ is the time in years. Here, $P = 64$, $r=0.5$ (since 50% = 0.5), and $t = 6$.

Step2: Substitute the values into the formula

$A=64\times(1 + 0.5)^6$.
First, calculate $(1 + 0.5)^6$. Since $1+0.5 = 1.5$, we have $1.5^6=1.5\times1.5\times1.5\times1.5\times1.5\times1.5 = 11.390625$.

Step3: Calculate the final amount

$A = 64\times11.390625$.
$64\times11.390625=729$.

Answer:

729