A certain type of bacteria is growing at an exponential rate that can be modeled by the equation y=ae^kt, where t represents the number of hours. There are 300 bacteria initially, and 1500 bacteria 5 hours later.

Question

Find the rate of growth, k, of the bacteria.

Write the equation that can be model the growth of the bacteria at time, t.

Answer 1

1500 = 300 e^(k * 5)

ln(5) = 5 k

k = 32.2% / hr

y(t) = 300 e^(.322 t)