The number of bacteria in a culture is increasing according

The number of bacteria in a culture is increasing according to the law of exponential growth. After 2 hours, there are 50 bacteria, and after 4 hours, there are 200 bacteria. How many bacteria will there be after 7 hours? bacteria

Solution

exponential growth model is y =Ae^kt

t =2 , y =50

50=Ae^2k

t =4 , y=200

200=Ae^4k

200/50=Ae^4k/Ae^2k

4=e^2k

2k=ln(4)

k=(1/2)ln(4)

k=ln(2)

t =2 , y =50

50=Ae^2ln(2)

50=Ae^ln(4)

50=A*4

4A=50

A=50/4

A=12.5

y =12.5e^t(ln(2))

after 7 hours, t =7

y =12.5e^7(ln(2))

y =12.5e^{(ln(2^7))}

y =12.5*2⁷

y=1600

after 7 hours there are 1600 bacteria