A population of insects increases at a rate of 250 + 16t +0.3t^2 insects per day. Find the insect population after 3 days, assuming that there are 40 insects at t=0.
Well, I'm no insect expert, but I do know a thing or two about numbers. Let's take this step by step.
First, we need to find the number of insects after 3 days. To do that, we need to use the given formula: population = 250 + 16t + 0.3t^2.
Plug in t=3 into the formula and let's calculate it together:
Population after 3 days = 250 + 16(3) + 0.3(3)^2
Now let's do the math:
Population after 3 days = 250 + 48 + 0.3(9)
= 250 + 48 + 2.7
= 298 + 2.7
= 300.7
Hence, the insect population after 3 days, assuming an initial population of 40 insects, is approximately 300.7 insects. Who knew insects could multiply so quickly? It's like they have their own version of the "Fast and the Furious"!
To find the insect population after 3 days, we need to evaluate the given equation at t = 3.
Given equation: P(t) = 250 + 16t + 0.3t^2
Substituting t = 3 into the equation:
P(3) = 250 + 16(3) + 0.3(3)^2
= 250 + 48 + 0.3(9)
= 250 + 48 + 2.7
= 298 + 2.7
= 300.7
Therefore, the insect population after 3 days is approximately 300.7 insects.
To find the insect population after 3 days, we need to evaluate the given population growth function at t = 3.
The population growth function is given as:
P(t) = 250 + 16t + 0.3t^2
First, let's substitute t = 3 into the equation to find the population after 3 days:
P(3) = 250 + 16(3) + 0.3(3)^2
= 250 + 48 + 0.3(9)
= 250 + 48 + 2.7
= 298 + 2.7
= 300.7
Therefore, the insect population after 3 days, assuming there are 40 insects at t = 0, is approximately 300.7 insects.
d(Insects)/dt = 250 + 16t + .3t^2
so Insects = 250t + 8t^2 + .1t^3 + c
when t=0, Insects = 40, so c = 40
Insects = 250t + 8t^2 + .1t^3 + 40
when t = 3
Insects = 750 + 72 + 2.7 + 40
= appr 865