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:
2 hours
Step-by-step explanation:
270 = (70+65) * t
270= 135t
t = 2
Answer:
They are dependent events. Event A is choosing one musician while Event B is choosing another musician. THey are ALL musicians, no matter what instrument they play, we just know that there are 7 musicians in total. Therefore, the events are dependent because after choosing one musician, you would have 6 musicians left, instead of 7.
Step-by-step explanation:
Answer:
y = -5x + 1
Step-by-step explanation:
y - 6 = -5 (x + 1)
distribute -5 (x + 1) by multiplying
y - 6 = -5x - 5
than add 6 to both sides
y = -5x + 1
<span>
<span><span>
x
y=2*(0.5)^x
</span><span>-10
2048
</span>
<span>
-9
1024
</span>
<span>
-8
512
</span>
<span>
-7
256
</span>
<span>
-6
128
</span>
<span>
-5
64
</span>
<span>
-4
32
</span>
<span>
-3
16
</span><span>-2
8
</span>
<span>
-1
4
</span>
<span>
0
2
</span>
<span>
1
1
</span>
<span>
2
0.5
</span>
<span>
3
0.25
</span>
<span>
4
0.125
</span>
<span>
5
0.0625
</span>
<span>
6
0.03125
</span>
<span>
7
0.015625
</span>
<span>
8
0.0078125
</span>
<span>
9
0.00390625
</span>
<span>
10
0.00195313
As x goes to negative infinity the function grows to infinity.
As x grows to infinity the function decreases an approximate to zero. </span></span></span>
