A population of a particular yeast cell develops with a constant relative growth rate of 0.4225 per hour. The initial population consists of 3.9 million cells. Find the population size (in millions of cells) after 3 hours. (Round your answer to one decimal place.)

The exponential function is often used to model the growth or decay of a population

The population size of the yeast cell after 3 hours is 7.9 million

The given parameters are:

--- initial number of cells

--- rate

The nth term of an exponential function is:

After 3 hours; n = 3

So, we have:

Substitute values for a and r

Hence, the population size of the yeast cell after 3 hours is 7.9 million

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The population after 3 hours is 13.9 mill.

Step-by-step explanation:

When we have an exponential with:

A  = initial population.

r = constant relative growth rate:

t = time.

The function that models this is:

P(t) = A*e^(k*t)

In this case we know that:

A = 3.9 mill.

r = 0.4225 1.

Then the function that models the population of this yeast cell is:

P(t) = (3.9 mill)*e^(0.4225*t)

where t represents the time in hours.

Then if we want to know the population after 3 hours, we should replace t by 3.

P(3) = (3.9 mill)*e^(0.4225*3) = 13.85 mill.

And we want to round our answer to one decimal place, then we must look at the second decimal place, we can see that is a 5, so we should round up.

The population after 3 hours is 13.9 mill.

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