The population for a city is 39,194 and grows continuously at a rate of 6.9% each year. What is the approximate population in 17 years?
My answer is 121,854
looks good
I don't get that ....
Population = 39194 e^(17*.069)
= 39194 e^1.173
= 39194*3.23167...
= appr 126,662
at just 6.9% compounded annually we would have
39164(1.069)^17 = 121,854 , which is your answer
you missed the part about "continuous" growth.
in questions such as population growth, the growth is taking place continuously, unlike a bank account where your balance "jumps" after certain interest periods.
Thank you
To calculate the approximate population in 17 years, you can use the formula for exponential growth:
P = P0 * e^(rt)
Where:
P: Final population
P0: Initial population
r: Growth rate (as a decimal)
t: Time in years
In this case, the initial population (P0) is 39,194 and the growth rate (r) is 6.9% per year (or 0.069 as a decimal). We want to find the population after 17 years (t = 17).
Plugging the values into the formula, we get:
P = 39,194 * e^(0.069 * 17)
Calculating the exponent:
P ≈ 39,194 * e^1.173
Using a calculator or a mathematical software, we find:
P ≈ 39,194 * 3.227717
Calculating further:
P ≈ 126,262.509
Therefore, the approximate population in 17 years would be around 126,263, not 121,854 as you mentioned.