Answer:
The exponential model n(t) is [tex]n(t) = 46(1.1487)^t[/tex]
Step-by-step explanation:
Exponential model of population growth:
An exponential model for population growth has the following model:
[tex]n(t) = n(0)(1+r)^t[/tex]
In which n(0) is the initial value and r is the growth rate, as a decimal.
Observed to double every 5 hours.
This means that [tex]n(5) = 2n(0)[/tex]
We use this to find 1 + r. So
[tex]n(t) = n(0)(1+r)^t[/tex]
[tex]2n(0) = n(0)(1+r)^5[/tex]
[tex](1+r)^5 = 2[/tex]
[tex]\sqrt[5]{(1+r)^5} = \sqrt[5]{2}[/tex]
[tex]1 + r = 2^{\frac{1}{5}}[/tex]
[tex]1 + r = 1.1487[/tex]
So
[tex]n(t) = n(0)(1+r)^t[/tex]
[tex]n(t) = n(0)(1.1487)^t[/tex]
Initially has 45 bacteria
This means that [tex]n(0) = 45[/tex]. So
[tex]n(t) = n(0)(1.1487)^t[/tex]
[tex]n(t) = 46(1.1487)^t[/tex]
The exponential model n(t) is [tex]n(t) = 46(1.1487)^t[/tex]
