The population of Adamsville grew from 10,000 to 15,000 in 7 years. Assuming uninhibited exponential​ growth, what is the expected population in an additional 4 ​years?

Answer 1

Remember the formula for population growth is A=A₀e^rt. A is the new population, A₀ is the initial population, r is the growth rate and t is the time. You first need to find the growth rate or r. So you need to rearrange your growth formula to solve for r. It would look something like: r=ln (A/A₀)/t. Divide both sides by A₀, take the natural log (ln) on both sides to get rid of the e and finally divide by t. Simply substitute the appropriate values and you will get r which is approximately 0.0579. Finally in order to find the population after an additional four years, simply add 4 years to the 7 years which will give you a total of 11 years and plug it back into the original problem. It will look sometime like this: A=10,000e^(0.0579)(11). That means in 11 years, the population will be about 20,063.