I need help working out this problem.

Question

The population of a colony of bacteria is decaying exponential according to the function below, where t is the time in minutes. How many minutes will it take for the colony to drop to 50?

Formula = B(t) = 2000*e^-0.3t

Answer 1

Step 1:

B(t) = 2000*e^-0.3t

Here B(t) is the  population of a colony of bacteria and t is the time.

Substitute 50 for  B(t) .

50 = 2000*e^-0.3t

Divide each side by 2000.

(50/2000) = e^-0.3t

0.025 =  e^-0.3t

Apply natural logarithms both sides

ln (0.025) = ​ln ( e^-0.3t)

From the logarithmic power law : ln a^m =m ln a

ln (0.025) =-0.3t ​ln ( e)

-3.69 = -0.3 t

t =12.29 min

Solution:

Time for the colony to drop to 50 is 12.29 min