math word problem help

Question

The number of bacteria in a certain culture is given by the function B(t)=10000e^.04t where t represents time in hours. How long will it take for the number of bacteria to reach 15,000? Round to the nearest hundredth.

Answer 1

B(t) = 10000 e^(0.04t), t in hours

 

At unknown time T (hours),

 

B(T) = 15000

 

B(T) = 10000 e^(0.04T) 

 

15000 = 10000 e^(0.04T)

 

T = [ln(15000/10000)] / (0.04) ≅ 10.14 hours

 

Test the answer:

 

10000 e^[(0.04)(10.14)] ≅ 15002.02 ≅ 15000

Answer 2

Maria,

in this problem we are looking for t

we are given B at a certain time we don't know

using the equation B(t)=10000e^0.04t

15000=10000e^0.04t

1.5=e^0.04t

ln(1.5)=0.04t

t=ln(1.5)/0.04

use calculator to get 

t=10.14