SOLUTION: On Monday, Lassister began monitoring the size of a bacteria colony. He noted that the mass of the colony grew from 5 grams at 8am to 6.5 grams at 2 PM. a) find the value for k a

Question 1034815: On Monday, Lassister began monitoring the size of a bacteria colony. He noted that the mass of the colony grew from 5 grams at 8am to 6.5 grams at 2 PM.
a) find the value for k and write an exponential growth function that estimates the mass M of the bacteria colony t hours after 8 AM Monday.
b) What will the mass be at 6 PM Monday?
c) To the nearest hour, at what time will the mass of the growing colony reach 15 grams?
please explain.

Found 2 solutions by jorel1380, josgarithmetic:
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
The formula for the growth rate is FA(final amount)=IA(initial amount)*(1+r(growth rate))^t. So:
a)6.5=5*(1+r)^6
1.3=(1+r)^6
1.3^.166666667=1+r
1+r=1.0446975079232772081587297735437
r=.0446975079232772081587297735437 as the growth rate of the bacteria. So:
M(1)=M(0)(1.044697508)^t
b)M=5*(1.044697508)^10
M=5*1.5484799527553624553339254907836=7.742399763776812276669627453918 gms. ☺☺☺☺
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
a) find the value for k and write an exponential growth function that estimates the mass M of the bacteria colony t hours after 8 AM Monday.
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p=5 grams, t is time in hours, k is a constant.

Given that M=6.5, p=5, t=6,

Growth model may be restated as .
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