Answer :
We are given the population model
[tex]$$
p(t) = 3125(1.03)^t,
$$[/tex]
where [tex]$t$[/tex] is the number of years since 2000.
1. To find the meaning of the number [tex]$3125$[/tex], we substitute [tex]$t = 0$[/tex] (the year 2000) into the function:
[tex]$$
p(0)=3125(1.03)^0.
$$[/tex]
2. Since any number raised to the power [tex]$0$[/tex] is [tex]$1$[/tex], we have
[tex]$$
(1.03)^0 = 1.
$$[/tex]
Thus,
[tex]$$
p(0) = 3125 \times 1 = 3125.
$$[/tex]
3. This value, [tex]$3125$[/tex], represents the population of the town in the year 2000.
Therefore, the number [tex]$3125$[/tex] is the population in the year 2000, which corresponds to option B.
[tex]$$
p(t) = 3125(1.03)^t,
$$[/tex]
where [tex]$t$[/tex] is the number of years since 2000.
1. To find the meaning of the number [tex]$3125$[/tex], we substitute [tex]$t = 0$[/tex] (the year 2000) into the function:
[tex]$$
p(0)=3125(1.03)^0.
$$[/tex]
2. Since any number raised to the power [tex]$0$[/tex] is [tex]$1$[/tex], we have
[tex]$$
(1.03)^0 = 1.
$$[/tex]
Thus,
[tex]$$
p(0) = 3125 \times 1 = 3125.
$$[/tex]
3. This value, [tex]$3125$[/tex], represents the population of the town in the year 2000.
Therefore, the number [tex]$3125$[/tex] is the population in the year 2000, which corresponds to option B.
