The population of Integraton (in millions) at time t (in years) is P(t) = 3.5e0.07t, where t = 0 is the year 2000.

Question

The population of Integraton (in millions) at time t (in years) is P(t) = 3.5e^0.07t, where t = 0 is the year 2000.

What is the population at time t = 0?

P(0) = ? million

When will the population double from its size at t = 0?

t = ? years

Answer 1

When t = 0:

P(0) = 3.5 e⁰ = 3.5

When will the population double from its initial value?

7 = 3.5 e^0.07t

2 = e^0.07t

ln (2) = ln (e^0.07t)

ln(2) = 0.07t ln(e) [ln(e) = 1]

t = ln(2)/0.07

Take a look at this graph to gain a better understanding:

desmos.com/calculator/ibrtzz3ua4

Answer 2

P(0) = 3.5e^(0.07)(0)

0 = 3.5e^0.07t, solve for t

Any questions?