Sure, let's solve this problem step-by-step.
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]
Hence, the correct answer is:
C. 60
