A town has a population of 10000 and grows at 2.5% every year. What will be the population after 7 years, to the nearest whole number?

Question

A town has a population of 10000 and grows at 2.5% every year. What will be the population after 7 years, to the nearest whole number?

i'm typically really good at math (i'm even in scholarship algebra) i just need a little help...

how do you multiply a percentage? or do you not? or...what...?

Answer 1

The expectation is that you will set up an exponential function. If a quantity increases at a rate of 2.5%, here is how you would determine the new amount. Q + .025Q = 1.025Q (converted the percentage to a decimal).

The exponential function takes the form y = ab^x where a is the initial amount, b is the base, x is time (you could use t for time). and y in the new amount. Note that after 1 year the new amount will be increased by 2.5% again (and so on).

The exponential function for this problem:

A(x) = 10000(1.025)^x (note that when x = 0, A(x) does equal 10000 (the initial amount).

To determine what the population will be after 7 years:

A(7) = 10000(1.025)⁷ (the expectation is that you will determine the nearest whole number after performing this calculation).

Check out the following on Desmos:

desmos.com/calculator/mdadxd5nsv

Answer 2

Hi Zachary E

Since you are given a starting population, growth rate per year and asked to determine an amount after a given period of time, sounds like you have an exponential growth problem, for which there are several formulas. You did not specifically say continuous and I assume you are referring to town’s human population, based on the information given I would recommend the following:

f(x) = a(1 + r)^x

Where

a = Starting Population = 10,000

(1 + r) = Growth factor for positive growth

r = rate of increase 2.5% written as a decimal

x = time, time is in years 7 for your problem above

f(x) = the population after 7 years

f(x) = 10000(1 + 0.025)⁷

f(x) = 10000(1.025)⁷

f(x) = 11886. 86

f(x) = 11886 because there is no 0.86 person

You can look up Exponential Growth formulas online or in your text and you can graph the function above

I hope this helps