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 35,230
disregard I posted correctly in a new one
To find the approximate population in 17 years, we can use the formula for exponential growth:
P(t) = P0 * e^(r * t)
Where:
P(t) = population after time t
P0 = initial population
r = growth rate
t = time elapsed
In this case, the initial population (P0) is 39,194, the growth rate (r) is 6.9% or 0.069 in decimal form, and the time elapsed (t) is 17 years.
Plugging those values into the formula:
P(17) = 39,194 * e^(0.069 * 17)
Now, we need to calculate e^(0.069 * 17). We can use a calculator or a math library function to find this value. Calculating it gives us:
e^(0.069 * 17) = 2.723
Now we can substitute this value back into the formula:
P(17) = 39,194 * 2.723
Calculating this gives us:
P(17) ≈ 106,872
So, the approximate population in 17 years is 106,872, not 35,230 as you previously mentioned.