32 + (5 − 2) ⋅ 4 − 6 over 3
=32 + 3 ⋅ 4 − 6/3
=32 + 12− 2
=44 - 2
= 42
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.
note: 5≠20
also, if you multiply both sides of an inequality by a negative number, you flip te direction of the inequality sign
example: 3<5, multiply by -1, -3>-5
so given
-2<3
multiply both ides by -5 and fip sign
remember that (-)(-)=(-) and (+)(-)=(-)(+)=(-)
10>-15
4th option is answer
Answer:
Step-by-step explanation:

This is a geometric progression pattern with the common ratio of negative 0.5.
The next three would be -0.5, followed by 0.25, followed by -0.125