1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
just olya [345]
3 years ago
8

When records were first kept (t=0), the population of a rural town was 260 people. During the following years, the population gr

ew at a rate of P'(t) = 45(1+sqrt(t)).
a) what is the population after 15 years?
b) find the popuation P(t) at any time t > 0.
Mathematics
1 answer:
Firdavs [7]3 years ago
5 0

Answer:

(a) The population after 15 years is 2678.

(b)Therefore the population P(t) at any time t>0 is

P(t)= 45t+30 {t^{\frac32}}+260

Step-by-step explanation:

Given that,

The population grew at a rate of

P'(t)=45(1+\sqrt t)

Integrating both sides

\int P'(t) dt=\int 45(1+\sqrt t)dt

\Rightarrow \int P'(t) dt=\int (45+45\sqrt t)dt

\Rightarrow \int P'(t) dt=\int 45\ dt+\int 45\sqrt t\ dt

\Rightarrow P(t)= 45t+45\  \frac{t^{\frac12+1}}{\frac12+1}+c              [ c is integration constant]

\Rightarrow P(t)= 45t+45\  \frac{t^{\frac32}}{\frac32}+c

\Rightarrow P(t)= 45t+45\times\frac 23 \times {t^{\frac32}}+c

\Rightarrow P(t)= 45t+30 {t^{\frac32}}+c

When t=0 , P(0)= 260

\therefore 260= 45\times0+30\times {0^{\frac32}}+c

\Rightarrow c=260

\therefore P(t)= 45t+30 {t^{\frac32}}+260

Therefore the population P(t) at any time t>0 is

P(t)= 45t+30 {t^{\frac32}}+260

To find the population after 15 years, we need to plug t=15 in the above expression.

P(15)=( 45\times 15)+30( {15^{\frac32}})+260

         ≈2678

The population after 15 years is 2678.

You might be interested in
Shenelle has 100100100 meters of fencing to build a rectangular garden. the garden's area (in square meters) as a function of th
cluponka [151]
Area as a function of width, w is:
a(w)=(w-25)^2+625
for maximum area, the width will be:
a'(w)=2(w-25)+0=0
solving for w we egt
2w-50=0
2w=50
w=25 m
given that the perimeter is 100, the length will be:
100=2(L+W)
solving for L we get:
L=50-W
but W=25m
hence
L=50-25=25 m
thus the maximum area will be:
A=L*W=25*25=625m^2

8 0
3 years ago
Read 2 more answers
What’s the area of the shaded region?
Leni [432]

Answer:

217.04 cm²

Step-by-step explanation:

We should first calculate the area of the rectangle:

A= 14*21 =294cm²

then we should substract the area of the half-cercle :

A'= (7²*π)/2=76.96 cm²

then the area of the shaded area is :

A"= 294-76.96= 217.04 cm²

5 0
3 years ago
According to the school survey,12% of the students at Rockwood Junior High School speak Spanish.There are 36 students at the sch
alexira [117]
Well the answer is 300 hundred students because there is 36 that makes 12% then to find 100% you need to do 12/36= 100/x doing this given x = to 300 total
8 0
3 years ago
Solve the equation p=2q + 2w for q.
elena-s [515]

Answer:

q =  1 /2 p − w

Step-by-step explanation:

4 0
4 years ago
A. k/5 = 3; k=<br> B. 3.5d = 70; d=<br> C. 4 1/2 = 1 1/2n; n=<br><br> Solve each equation.
Kryger [21]

Answer:

Step-by-step explanation:

A. k/5 = 3:  Isolate k by multiplying both sides of this equation by 5:

k = 15

       

B. 3.5d = 70;  Divide both sides by 3.5, obtaining d = 20

C. 4 1/2 = 1 1/2n;   Rewrite 4 1/2 and 1 1/2 as improper fractions:

  9/2 = (3/2)n.  Now multiply both sides by (2/3):  3 = n

8 0
3 years ago
Read 2 more answers
Other questions:
  • All the yellow surfaces on this ferris wheel pod
    13·1 answer
  • How to spell 6007200 in word form
    9·1 answer
  • Is the product 1.23 x 8 greater than or less than 8? Explain.
    8·2 answers
  • Rita read a book with 973 pages in one week. if she read the same number of pages each day how many pages did rita read each day
    5·1 answer
  • Halle has 36 feathers, 48 acorns, and 60 gates. She wants to pull all of these items into bowls with the same number of feathers
    11·2 answers
  • in one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean
    13·1 answer
  • ABC is an isosceles triangle with AB=BC ACD is a straight line work out the size of BCD
    11·1 answer
  • 10 is what percent of 625
    9·2 answers
  • Graph each transformation, g(x), and write the equation for the transformed function​
    12·1 answer
  • A(x+b)-c=d<br> solve the following equation for x
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!