Find the continuous percent growth rate and formula of the function

Question

Doubling time given: 12 days

-Use the doubling time to find the continuous percent growth rate. Round to two decimal places.

-Use the continuous growth rate to find a formula for the function. Assume P(0)=30. Round to 4 decimal places.

Extra points on graph given: (12,60) (24,120)

Answer 1

P(0) = 30

doubling time = 12 days

(12, 60), (24,120) are points on the graph

P = Ae^rt

30 = Ae^r(0) =A = 30

60 = 30e^12r

2 = e^12r

take natural logs of both sides

ln2 = 12r

r = ln2/12 = about 0.057762265=about 5.7762 %

P =30e^0.0578t where t is measured in days and e = about 2.71828

P(24) =30e^.0578(24)= about 120