State whether the growth (or decay) is linear or exponential, and answer the associated question. The population of Jamestown is increasing at a rate of 2.5% each year. If the population is 25,000 today, what will it be in 2 years?
population = 25000(1.025)^2
= ....
exponential
In this scenario, the growth is exponential since the population is increasing at a certain percentage each year.
To find the population in 2 years, we can use the following formula:
Population after t years = Initial population * (1 + growth rate/100)^t
Given an initial population of 25,000 and a growth rate of 2.5%, we can substitute these values into the formula:
Population after 2 years = 25,000 * (1 + 2.5/100)^2
Calculating the result:
Population after 2 years = 25,000 * (1 + 0.025)^2
= 25,000 * (1.025)^2
= 25,000 * 1.050625
= 26,265.63
Therefore, the population of Jamestown will be approximately 26,265 in 2 years.
To determine if the growth is linear or exponential, we need to check if the growth rate is constant or if it is based on a percentage increase over time.
In this case, the population of Jamestown is increasing at a rate of 2.5% each year. This indicates that the growth is exponential, not linear, because the growth rate is a percentage increase that is being compounded over time.
To find the population in 2 years, we can use the exponential growth formula:
Population = Initial Population * (1 + Growth Rate/100)^Time
In this case, the initial population is 25,000, the growth rate is 2.5%, and the time is 2 years.
Plugging in these values, we get:
Population = 25,000 * (1 + 2.5/100)^2
Calculating this expression:
Population = 25,000 * (1 + 0.025)^2
Population = 25,000 * (1.025)^2
Population ≈ 25,000 * 1.050625
Population ≈ 26,265.63
Therefore, the population of Jamestown in 2 years will be approximately 26,265.63.