Answer: 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.
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:
[tex]\mathbf{a = 3.9m}[/tex] --- initial number of cells
[tex]\mathbf{r = 0.4225/hr}[/tex] --- rate
The nth term of an exponential function is:
[tex]\mathbf{f(n) = a(1 + r)^{n-1}}[/tex]
After 3 hours; n = 3
So, we have:
[tex]\mathbf{f(3) = a(1 + r)^{3-1}}[/tex]
Substitute values for a and r
[tex]\mathbf{f(3) = 3.9(1 + 0.4225)^{3-1}}[/tex]
[tex]\mathbf{f(3) = 3.9(1 + 0.4225)^{2}}[/tex]
[tex]\mathbf{f(3) = 3.9 \times (1.4225)^{2}}[/tex]
[tex]\mathbf{f(3) = 7.9}[/tex]
Hence, the population size of the yeast cell after 3 hours is 7.9 million
Read more about exponential functions at:
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