Given that the starting population, [tex]$N(0)$[/tex], is 10 and has a growth rate, [tex]$m$[/tex], of 2 individuals per unit of time, what will the population be at 25 units of time?
The problem is based on the linear growth formula for population: [tex]\[
N(t) = m t + N(0)
\][/tex] where: - [tex]\(N(t)\)[/tex] represents the population at time [tex]\(t\)[/tex] - [tex]\(m\)[/tex] is the growth rate (individuals per unit of time) - [tex]\(N(0)\)[/tex] is the starting population at time [tex]\(t=0\)[/tex]
Given values: - The starting population [tex]\(N(0)\)[/tex] is 10 - The growth rate [tex]\(m\)[/tex] is 2 individuals per unit of time - The time [tex]\(t\)[/tex] is 25 units
We need to find the population [tex]\(N(t)\)[/tex] at [tex]\(t = 25\)[/tex]: [tex]\[
N(t) = m \cdot t + N(0)
\][/tex]
Substituting the given values into the formula: [tex]\[
N(25) = 2 \cdot 25 + 10
\][/tex]
Now, let's perform the calculations step-by-step:
1. Multiply the growth rate [tex]\(m\)[/tex] by the time [tex]\(t\)[/tex]: [tex]\[
2 \cdot 25 = 50
\][/tex]
2. Add the starting population [tex]\(N(0)\)[/tex] to the result: [tex]\[
50 + 10 = 60
\][/tex]
Therefore, the population at 25 units of time is: [tex]\[
N(25) = 60
\][/tex]
