Explanation:
a.
correct, the population was 18.5 million in 2000.
why ?
t = years after 2000.
so, if the year is 2000, t = 0.
A(0) = 18.5e^(0.1708 × 0)
you remember, a⁰ = 1 for any a.
so,
A(0) = 18.5×e⁰ = 18.5×1 = 18.5 million.
b.
we need to find the value of t for which A(t) = 26.6.
26.6 = 18.5e^(0.1708 × t)
26.6/18.5 = e^(0.1708 × t)
ln(26.6/18.5) = 0.1708 × t
t = ln(26.6/18.5)/0.1708 = 2.126115244... years
≈ 2 years
2 years after 2000 is 2002.
it will reach 26.6 million in the year 2002.