A biologist recorded a count of 360 bacteria present in a culture after 5 minutes and 1000 bacteria present after 20 minutes. Write the exponential equation representing this scenario modeled as a continuous growth model.

And our exponential model would be:

Step-by-step explanation:

We want to adjust an exponential model given by this general expression:

Where A(t) represent the number of bacteria after some t minuts

t represent the time in minutes

represent the initial amount of bacteria

represent the growth/decay rate

For this problem we know the following two conditions:

Using the first condition we have this:

We can solve for the initial amount and we got:

  (1)

Now using the second condition we have this:

 (2)

Replacing equation (1) into (2) we have this:

  (3)

Now we can divide both sides by 360 and we got:

Now we can apply natural log on both sides and we got:

And solving for r we got:

And replacing this value of r into equation (1) we got:

And our exponential model would be:

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step-by-step explanation: