Question

Park service personnel are trying to increase the size of the bison population of a large park. If 140 bison currently live in the park, and if the population's rate of growth is 1% annually, find how many bison (rounded to the nearest whole) there should be in 30 years. Use y = 140(2.7)^0.01t, where the t represents time in years

Answer 1

Answer:

$y(t) = 140 (2.7)^{0.01t}$

Where t represent the time in years

For this case this model follows the general model given by:

$y = a b^t$

Where a = 140 represent the initial amount of bisons and y the number of bisons after t years and b = 2.7 represent the growth rate

For this case we want to find the value of y when t =30, and if we replace the value of t =30 in our function we got:

$y(30) = 140(2.7)^{0.01*30} = 188.598$

And if we round to the nearest whole number we got 189 bisons after 30 years

Step-by-step explanation:

For this case we have the following function given:

$y(t) = 140 (2.7)^{0.01t}$

Where t represent the time in years

For this case this model follows the general model given by:

$y = a b^t$

Where a = 140 represent the initial amount of bisons and y the number of bisons after t years and b = 2.7 represent the growth rate

For this case we want to find the value of y when t =30, and if we replace the value of t =30 in our function we got:

$y(30) = 140(2.7)^{0.01*30} = 188.598$

And if we round to the nearest whole number we got 189 bisons after 30 years