The rat population in a major metropolitan city is given by the formula n(t)=82e^0.025t where t is measured in years since 1990 and n is measured in millions.
(a) What was the rat population in 1990?
(b) What is the rat population going to be in the year 2007?
you know, you post a lot of questions of varying degrees of difficulty, but you never seem to think it necessary to show that you have actually tried to solve them.
No ideas at all on this one? It's a pretty basic problem in exponentials. I mean, they've actually provided the formula, so what's the trouble?
and there are plenty of web sites like desmos and wolframalpha where you can confirm your solution.
i have tried to solve them but after entering the answer and getting ti wrong twice i wanted help so I don't loose credit
No cheating.
To find the rat population in 1990, we need to substitute t = 0 into the given formula and solve for n(t).
(a) Rat population in 1990 (t = 0):
n(0) = 82e^(0.025 * 0)
Since any number raised to the power of zero is 1, the equation simplifies to:
n(0) = 82 * 1
Therefore, the rat population in 1990 was 82 million.
To find the rat population in the year 2007, we need to substitute t = 2007 - 1990 into the given formula and solve for n(t).
(b) Rat population in the year 2007 (t = 2007 - 1990 = 17):
n(17) = 82e^(0.025 * 17)
Using a calculator or math software, we can approximate this value:
n(17) ≈ 82 * 2.71^(0.025 * 17)
Evaluating the expression, we get:
n(17) ≈ 82 * 2.71^0.425
n(17) ≈ 82 * 1.293
Therefore, the rat population in the year 2007 is approximately 106 million.