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Katen [24]
2 years ago
14

The fox population in a certain region has a continuous growth rate of 7 percent per year. It is estimated that the population i

n the year 2000 was 14300. (a) Find a function that models the population t years after 2000 (t=0 for 2000). Hint: Use an exponential function with base e. Your answer is P(t)
Mathematics
1 answer:
rjkz [21]2 years ago
7 0

Answer:

P(t) = 14300e^0.07t

Step-by-step explanation:

Let :

Population as a function of years, t = P(t) ;

Growth rate, r = 7%

Estimated population on year 2000 = Initial population = 14300

The given scenario can be modeled using an exponential function as the change in population is based in a certain percentage increase per period.

P(t) = Initial population*e^rt

P(t) = 14300*e^(0.07t)

P(t) = 14300e^0.07t

Where, t = number of years after year 2000.

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13) -3x - 4y = 8<br>-4x - 3y=6​
Dvinal [7]

Answer:

x = 0, y = -2

Step-by-step explanation:

-3x - 4y = 8  (1)

-4x - 3y=6​ (2)

Multiply (1) by -4 and (2) by -3, we have:

12x + 16y = - 32  (3)

12x + 9y= -18​ (4)

Subtract (4) from (3), we have:

(12x + 16y) - (12x + 9y) = - 32  - (-18)

<=> 7y = - 14

=> y = - 2

Replace y with - 2 in (3), we have x = 0

6 0
3 years ago
A study of consumer smoking habits includes A people in the 18-22 age bracket (B of whom smoke), C people in the 23-30 age brack
madreJ [45]

The correct question is:

A study of consumer smoking habits includes 167 people in the 18-22 age bracket (59 of whom smoke), 148 people in the 23-30 age bracket (31 of whom smoke), and 85 people in the 31-40 age bracket (23 of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 23-30 or smokes

Answer:

The probability of getting someone who is age 23-30 or smokes = 0.575

Step-by-step explanation:

We are given;

Number consumers of age 18 - 22 = 167

Number of consumers of ages 22 - 30 = 148

Number of consumers of ages 31 - 40 = 85

Thus,total number of consumers in the survey = 167 + 148 + 85 = 400

We are also given;

Number consumers of age 18 - 22 who smoke = 59

Number of consumers of ages 22 - 30 who smoke = 31

Number of consumers of ages 31 - 40 who smoke = 23

Total number of people who smoke = 59 + 31 + 23 = 113

Let event A = someone of age 23-30 and event B = someone who smokes. Thus;

P(A) = 148/400

P(B) = 113/400

P(A & B) = 31/400

Now, from addition rule in sets which is given by;

P(A or B) = P (A) + P (B) – P (A and B)

We can now solve the question.

Thus;

P(A or B) = (148/400) + (113/400) - (31/400)

P(A or B) = 230/400 = 0.575

4 0
3 years ago
24 is 30% of what? <br><br> Help
Radda [10]
    <u>24</u> = <u>30</u>
      x = 100
 <u>30x</u> = <u>2400</u>
  30  =   30
      x = 80
4 0
3 years ago
The circle below is centered at the origin and has a radius of 4. What is its
BlackZzzverrR [31]

Answer:

Step-by-step explanation:

The standard form of a circle's equation is

(x-h)^2+(y-k)^2=r^2 where h and k are the circle's center and r is the radius. We are told, and we can see, that the center of the circle is (0, 0) so h = 0 and k = 0. The radius, given as 4, goes into the equation squared, so the equation is

(x-0)^2+(y-0)^2=16 which simplifies down to

x^2+y^2=16, choice C.

8 0
3 years ago
Read 2 more answers
Which equation is a point slope form equation for line AB ?
kap26 [50]

Answer:

y-5=\frac{3}{4}(x-6)

Step-by-step explanation:

we know that

The equation of a line in point slope form is equal to

y-y1=m(x-x1)

step 1

Find the slope m

we have the points

A(-2,-1),B(6,5)

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the values

m=\frac{5+1}{6+2}

m=\frac{6}{8}

simplify

m=\frac{3}{4}

step 2

Find the equation of the line

we have

(x1,y1)=(6,5)

m=\frac{3}{4}

substitute

y-y1=m(x-x1)

y-5=\frac{3}{4}(x-6)

3 0
3 years ago
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