A population of bacteria is growing according to the equation P ( t ) = 900 e^ 0.11 t . Use a graphing calculator to estimate when the population will exceed 1337.

Question

A population of bacteria is growing according to the equation P(t)=900e^0.11t

Use a graphing calculator to estimate when the population will exceed 1337.

t = 

Answer 1

I can't exactly run a graphing calculator for you, but we can do the following.

P(t) = 900*e^0.11t

If we want to know the time when P = 1337, we simply set this to 1337 and solve.

1337 = 900*e^0.11t (Divide both sides by 900)

1337/900 = e^0.11t (take the natural log of each side)

ln(1337/900) = ln(e^0.11t) and now the natural log cancels the exponentiation

ln(1337/900) = 0.11t (Divide each side by 0.11 to fully isolate t)

t = ln(1337/900)/0.11 which is approximately 3.598 of whatever unit t is in.