Help!!!!!
The population of a town was 5655 and 2010. The population grows at a rate of 1.4% annually. Use the exponential growth model to write an equation that estimates the population T years after 2010. Use the equation you wrote to estimate the population of the town in 2022. Show your work.

Question

contestada

Respuesta :

opudodennis opudodennis · Answer 1 · 2020-04-02T03:22:40+02:00

Answer:

6690

Step-by-step explanation:

Given the initial population as 5655 at time 2010, the growth rate as 1.4% and the final time as 2022.

-Exponential growth is expressed as:

[tex]A_t=A_oe^{kt}\\\\k-growth \ rate\\t-time\\A_o-Initial \ Population\\A_t-Pop \ at \ t[/tex]

#We substitute the given growth rate,1.4% and Initial population 5655 in the expression to find our function:

[tex]A_t=5655e^{0.014t}[/tex]

#We first determine the time elapsed between the initial and final times:

[tex]t=t_n-t_o\\\\=2022-2010\\\\=12[/tex]

#We substitute our values in the function to estimate the population in 2022:

[tex]A_t=A_oe^{kt}\\\\=5655e^{12\times 0.014}\\\\=6689.51\approx6690[/tex]

Hence, the estimate population in 2022 is 6690