Respuesta :
Answer:
[tex]P(t) = 880(1.4142)^{t}[/tex]
Step-by-step explanation:
The bacteria's population may be expressed by the following equation:
[tex]P(t) = P_{0}(1+r)^{t}[/tex]
In which [tex]P_{0}[/tex] is the initial population, and r is the growth rate, as a decimal.
A bacteria culture starts with 880 bacteria and grows at a rate proportional to its size. After 4 hours there will be 3520 bacteria.
This means that [tex]P_{0} = 880, P(4) = 3520[/tex].
(a) Express the population P after t hours as a function of t . Be sure to keep at least 4 significant figures on the growth rate.
We have to find the growth rate, which we do applying the value of P(4) to the equation.
[tex]P(t) = P_{0}(1+r)^{t}[/tex]
[tex]3520 = 880(1+r)^{4}[/tex]
[tex](1+r)^{4} = \frac{3520}{880}[/tex]
[tex](1+r)^{4} = 4[/tex]
Applying the fourth root to both sides of the equality.
[tex]1 + r = 1.4142[/tex]
[tex]r = 0.4142[/tex]
So the equation of P(t) is:
[tex]P(t) = 880(1.4142)^{t}[/tex]
