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:
Step-by-step explanation:
In order to find the slope of a line you must find where the points intersect, use the formula for slope, substitute values, and simplify if needed.
In this case we were already given the points for slope:
Slope formula:
Now substitute:
Solve using KCC: (Keep, Change, Change)
=
Because the slope isn't a negative you do not need to simplify the answer.
Hope this helps.
The answer to the problem is as follows:
x = sin(t/2)
<span>y = cos(t/2) </span>
<span>Square both equations and add to eliminate the parameter t: </span>
<span>x^2 + y^2 = sin^2(t/2) + cos^2(t/2) = 1 </span>
<span>The final step is translating the original parameter limits into limits on x and y. Over the -Pi to +Pi range of t, x varies from -1 to +1, whereas y varies from 0 to 1. Thus we have the semicircle in quadrants I and II: y >= 0.</span>
Answer:
y = (-2/3)x-3
Step-by-step explanation:
Hello:
equation is the line is : y = ax+b a is a slope
y = (-2/3)x+b
passing through the point (−3;−1) : -1 =(-2/3)(-3)+b so : b = -3
y = (-2/3)x-3
second solution : you can verify (-3 ; -1) in the equation : y = (-2/3)x-3
For this case we have the following table:
x f(x)
<span><span><span>0 2
</span><span>1 5
</span><span>2 10
</span><span>3 17
</span></span></span> The equation that best fits the data in the table, for this case, is given by a quadratic function.
<span><span><span> </span></span></span>The quadratic function in its standard form is:
f (x) = x2 + 2x + 2
Answer:
f (x) = x2 + 2x + 2
