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Angelina_Jolie [31]
3 years ago
13

The park service that administers a state park estimates that there are 495 deer in the park. They decide to remove deer accordi

ng to the differential equation dP/dt = −0.1P.
a. Show that the solution to the differential equation dP/dt = −0.1P is P = 495e^−0.1t , where t is measured in years and P is the population of deer. Use it to find the deer population in 5 years to the nearest deer.

b. After this 5-year period, no human intervention is taken and the deer population grows again. From that time, the deer population increases directly proportional to 650−P, where the constant of proportionality is k. Find an equation for the deer population P(t) in terms of t and k for this 5-year period.

c. Using the growth model from part b), 1 year later the deer population is 350. Find k.

d. Using the growth model from part b) and the value of k from part c), find lim t→∞ P(t)
Mathematics
1 answer:
Vlada [557]3 years ago
6 0

Answer:

your answer is (A.)

Step-by-step explanation:

You might be interested in
The image below is a kite. Find the value of x.
polet [3.4K]

Answer:

x=55.5

Step-by-step explanation:

2x=111

Isolate x by dividing both sides by 111

x=55.5

4 0
2 years ago
A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced.
zzz [600]

Answer:

CI=(66.54,78.46)                                  

Step-by-step explanation:

Given : A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced. The mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%. Assume the yields are independent and approximately normally distributed.

To find : A 99% confidence interval for the mean yield when the new catalyst is used ?

Solution :

Let X be the yield of the batches.

We have given, n=10 , \bar{X}=72.5\% , s=5.8%

Since the size of the sample is small.

We will use the student's t statistic to construct a 995 confidence interval.

\bar X\pm t_{n-1,\frac{\alpha}{2}}\frac{s}{\sqrt n}

From the t-table with 9 degree of freedom for \frac{\alpha}{2}=0.005

t_{n-1,\frac{\alpha}{2}}=t_{9,0.005}

t_{n-1,\frac{\alpha}{2}}=3.250

The 99% confidence interval is given by,

CI=72.5 \pm 3.25\frac{5.8}{\sqrt{10}}

CI=72.5 \pm 5.96

CI=(72.5+5.96),(72.5-5.96)

CI=(66.54,78.46)

8 0
3 years ago
What is the value of f(7.5) when f(x)=2x+7
Ivan

Hey there!!

Given :

f ( x ) = 2x + 7

Find f ( 7.5 )

Now, we will need to substitute the value of 7.5 in place of x

f(7.5) = 2(7.5) + 7

f(7.5) = 15 + 7

f(7.5) = 22

Hope my answer helps!


6 0
2 years ago
URGENT PLEASE HELP !!!!!
Mumz [18]

Answer:

Let P represent the number of pies sold and J represent the number of juices sold.

a)

The first equation for the sum of the sales:

P + J = 79

P = 79 - J

Next, for the sum of the amounts earned:

1.65P + 1.36J = 118.17

Substituting P,

1.65 (79 - J) + 1.36J = 118.17

J = 42

Using this value of J,

P = 79 - 42

P = 37

b)

Mr. Sanchez's class earned: 1.65 x 37 = $61.05

Mr. Kelly's class earned: 1.36 x 42 = $57.12

So Mr. Sanchez's class earned more money.

c) Mr. Sanchez's class earned:

61.05 - 57.12

= $3.93 more than Mr. Kelly's class

Step-by-step explanation:

:)

4 0
3 years ago
What is the y-intercept, and what does it represent?
ArbitrLikvidat [17]

Answer:

The y-intercept is where an equation's graph hits the y-axis. It represents the constant value, when x=0, the intercept is the constant

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
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