50 points to correct answer
1. the population of a town was 4000 in 2010. the population grows at a rate of 3.8% annually.
(a) use the exponential growth model to write an equation that estimates the population t years after 2010.
(a) estimate the population of the town in 2024. show your work.

answer:

(a)

(b) ≅ 6809

step-by-step explanation:

the exponential growth model applies to any situation where growth is proportional to the current size of the amount of interest. the exponential growth model is often used for real-life situations such as interest earned on an investment, human or animal population, bacterial growth, etc.

it is based on exponential growth, and it is applied to a magnitude such that its variation in time is proportional to its value, which implies that it grows faster and faster in time, according to the equation:

so, the population of a town was 4000 in 2010, and the population grows at a constant rate of 3.8%.

(a) using the exponential growth model we can write an equation that estimates the population in (t) years after2010.

where:

is the population in any year;

is the initial population in 2010;

is the growth constant of 3.8% or 0.038;

and is the time in a year elapsed.

substituting the values ​​we get:

which is the equation that estimates the population (t) years after 2010.

(b) estimate the population of the town in 2024.

from 2010 to 2024 will have elapsed 14 years.

so, substituting the values we get:

then, the estimate population of the town in 2024 is ≅ 6809

the answer is a

step-by-step explanation:

because if you put 1 in to the square root of x it equals 300.