The population N of a bacteria strain grows according to the

The population N of a bacteria strain grows according to the equation y = 200(2)^1.4t, where t is the time in hours. How many bacteria were there at the beginning of the experiment? How many bacteria will exist in ten hours? Estimate the number of bacteria two hours before the experiment started.

Solution

This equation os of the form

y=a b^x where a is the initial value

Therefore in the given equation 200 bacteria are there at the beginning of experiment.

b. y= 200 2 ^1.4t

when t=10 we get

y= 200 2 ^1.4×10 = 200 2¹⁴= 3276800

c. at t=-2

y=200 2 ^1.4*(-2) = 29