Question

The number of bacteria in a culture is given by the equation N = 8.4^t, where t is measured in hours. How many bacteria were present initially?​

Answer 1

(I will suppose that the actual equation is: N = 8*4^t instead of N = 8.4^t)

A general exponential growth can be written as:

f(x) = A*r^x

Where:

A is the initial amount.

r is the rate of growth

x is the variable.

Here we have the equation:

N = 8*4^t

Comparing this with the general form, we have:

Initial amount = 8

rate of growth = 4

variable = t

Then is easy to see that initially, there are 8 baceria present.

We also can see this if we evaluate the function in t = 0.

N(0) = 8*4^0 = 8*1 = 8

If instead, the function was:

N = 8.4^t

Then we can rewrite this as:

N = 1*(8.4)^t

And we will have:

initial amount = 1

rate of growth = 8.4

variable = t

Then in this case we have a single bacteria initially persent.