Question 37857: Memphis, Tennesse, is growing ata rate of 0.36% per year. Find how long, to the nearest tenth of a year it will take an initial population of 650,000 to increase to 700,000. Use the population growth formula y = ybase0e^kt. The answer is 20.6 years, I just don't know how to get to it.
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Okay, sure...yes the operating equation for exponential growth is
y = y0(e^kt)
Here y = 700000, y0 = 650000, k = .0036 and we need to find t, so plug in
700000 = 650000(e^(.0036t))
divide both sides by 650000
1.077 = e^(.0036t)
Now take the natural log of both sides
ln 1.077 = .0036t
and divide by .0036
t = ln(1.077) / .0036
t = 20.59 years
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