To solve this problem, we start with the given formula for population growth:
[tex]\[ N(t) = m \cdot t + N(0) \][/tex]
where:
- [tex]\( N(t) \)[/tex] is the population at time [tex]\( t \)[/tex],
- [tex]\( m \)[/tex] is the growth rate of the population (individuals per unit of time),
- [tex]\( t \)[/tex] is the time in units,
- [tex]\( N(0) \)[/tex] is the initial population at time [tex]\( t = 0 \)[/tex].
We are given the following values:
- The starting population [tex]\( N(0) \)[/tex] is 5 individuals.
- The growth rate [tex]\( m \)[/tex] is 2 individuals per unit of time.
- The time [tex]\( t \)[/tex] is 20 units.
Now, we substitute these values into the formula:
[tex]\[ N(t) = 2 \cdot 20 + 5 \][/tex]
First, we calculate the product of the growth rate and the time:
[tex]\[ 2 \cdot 20 = 40 \][/tex]
Next, we add the initial population to this product:
[tex]\[ 40 + 5 = 45 \][/tex]
Thus, the population at 20 units of time will be:
[tex]\[ N(20) = 45 \][/tex]
Therefore, the population at 20 units of time is 45 individuals.
