PLEASE HELP - The number of bacteria in a sample is increasing according to an exponential model.

Question

The number of bacteria in a sample is increasing according to an exponential model. After three hours, the sample contained 100 bacteria. After nine hours, the sample contained 400 bacteria. Write an exponential growth model for the number of bacteria in the sample after x hours.

Multiple Choice

a. P(x) = 100e(In(4)/6)x

b. P(x) = 25e(In(4)/6)x

c. P(x) = 50e(In(4x)/6)

d. P(x) = 50e(6/In(4))x

e. P(x) = 50e(In(4)/6)x

Answer 1

James is correct.

It's clear that the number of bacteria doubles every 3 years.

So t=3 100

t = 6 200

t = 9 400

working backwards to t=0 gives 50 at t=0.

So the exponential expression will be 50 (2^x/3)

50 because we have 50 bacteria at t=0

2 because it doubles

x/3 because it doubles every 3 years

This is equivalent to E

Answer 2

We assume the model is P(x)=a*e^(bx)

When x=3,   p(3)=a*e^(3b)=100

When x=9,  p(9)=a*e^(9b)=400

P(9)/P(3)= a*e^(9b) / (a*e^(3b) =400/100

e^(9b-3b)=4

e^(6b)=4 ----> e^(3b)=2

6b=ln (4)

b= ln (4) / 6

a*e^(3b)=100

a*2=100 

a=50

P(x)=50*e^(x*in(4) /6)

The answer is E