Exponential function showing relationship between y and t

Question

290000 people increase by 1.2% each year

Answer 1

y = 290000(1.012)^t

Answer 2

Hi June! It sounds like we need a function that satisfies the following points:

t = 0, y = 290000

t = 1 year, y = 293480 (290000 + 1.2% of that)

etc.

Since we aren't told what the base of the exponential function is, we should assume it is e. So our exponential function looks like this:

y(t) = y₀e^rt

y₀, the initial value, is 290000. We can use the next data point to find r:

293480 = 290000 e^r*1

1.012 = e^r

ln(1.012) = r

r is approximately 0.012

So y(t) = 290000e^0.012t