The question is incomplete. The complete question is :
The population of a certain town was 10,000 in 1990. The rate of change of a population, measured in hundreds of people per year, is modeled by P prime of t equals two-hundred times e to the 0.02t power, where t is measured in years since 1990. Discuss the meaning of the integral from zero to twenty of P prime of t, d t. Calculate the change in population between 1995 and 2000. Do we have enough information to calculate the population in 2020? If so, what is the population in 2020?
Solution :
According to the question,
The rate of change of population is given as :
in 1990.
Now integrating,
![$=\frac{200}{0.02}\left[e^{0.02(20)}-1\right]$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B200%7D%7B0.02%7D%5Cleft%5Be%5E%7B0.02%2820%29%7D-1%5Cright%5D%24)
![$=10,000[e^{0.4}-1]$](https://tex.z-dn.net/?f=%24%3D10%2C000%5Be%5E%7B0.4%7D-1%5D%24)
![$=10,000[0.49]$](https://tex.z-dn.net/?f=%24%3D10%2C000%5B0.49%5D%24)
=4900
This is initial population.
k is change in population.
So in 1995,
In 2000,
Therefore, the change in the population between 1995 and 2000 = 1,163.
Answer:
correct choice is 1st option
Step-by-step explanation:
Two given triangles have two pairs of congruent sides: one pair of length 7 units and second pair of length 8 units. The third side is common, i.e the lengths of third sides are equal too.
Use SSS theorem that states that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.
Thus, given triangles are congruent by SSS theorem.
Constant is occurring continuously over a period of time so C is the correct answer because C is constant for a period of time
Answer:
The larger acute angle is equal to 50.8 degrees.
Step-by-step explanation:
Let's solve for both of the acute angles for the purpose of checking our work at the end with angle A being the top angle and angle B being the one on the base of the triangle (that's not the 90 degrees one). Determining whether to use sin/cos/tan comes from SOH-CAH-TOA.
A = cos^-1 (2√6/2√15)
However, you need to move the radical out of the denominator by multiplying √15 to the numerator and denominator. You should come up with (2√90)/30. So,
A = cos^-1 (2√90/30) = 50.768 degrees.
B = sin^-1 (2√90/30) = 39.231 degrees.
Now, we can check the work by adding the 2 angles to 90 and, if it comes to 180, it's right.
cos^-1 (2√90/30) + sin^-1 (2√90/30) + 90 = 180.
If you have any questions on where I got a formula or any step, feel free to ask in the comments!
