MATHEMATICS COLLEGE

(1 point) The number of households with cable TV service in a certain community, N, begins at only 55 households and has seen a fivefold increase every 17 years. Give the constants a, b, and T so that N is represented by a function of the form N=abt/T, where t is the time in years since N was first measured.

Answers

Answer 1

Answer:

Answer:

a=55

b=5

T=17

Step-by-step explanation:

The general form of the equation is:

$N(t)=ab^{(t)/(T)}$

For t = 0:

$N(0)=ab^{(0)/(T)}\nN(0) = a = 55\na=55$

Since there has been a fivefold increase after 17 years, at t = 17, N(17) = 55*5

$N(17)=55b^{(17)/(T)}\n55*5 = 55b^{(17)/(T)}\nb^{(17)/(T)} = 5$

If at every 17*n years there in an increase of 5^n, one can deduct that the values for T and b are respectively 17 and 5:

$b^{(t)/(T)}= 5^{(17n)/(17)}$

Therefore, the function that represents N(t) is:

$N(t)=55*5^{(t)/(17)}$

Related Questions

Need help asap 6. Which line has a slope equal to 1?HELP ON 7 two
Convert 5 feet 4 inches to centimeters. (2.54 cm = 1 inch) *PLEASE HELPPPP
Consider a colony of E.Coli bacteria that is growing exponentially. A microbiologist finds that, initially, 1,000 bacteria are present and 50 minutes later there are 10,000 bacteria. a) Find expression for the number of bacteria Q(t) after t minutes. b) When will there be 1,000,000 bacteria?
I am probably just really dumb, but I don't understand the concept. The question is: -42v+33<8v+91. I am supposed to solve the inequality for v. Please give an explanation and not just an answer, I would really like to know how to do this.
Find the equation of a line containing the points (5,1) and (5,−4).

Find AC
What Is The Equation To AC?

Answers

Given:

Given that ABC is a right triangle.

The length of AB is 7 units.

The measure of ∠A is 65°

We need to determine the length of AC

Length of AC:

The length of AC can be determined using the trigonometric ratio.

Thus, we have;

$cos \ \theta=(adj)/(hyp)$

Where the value of $\theta$ is 65° and the side adjacent to the angle is AC and the side hypotenuse to the angle is AB.

Substituting the values, we have;

$cos \ 65^(\circ)=(AC)/(AB)$

Substituting AB = 7, we have;

$cos \ 65^(\circ)=(AC)/(7)$

Multiplying both sides by 7, we get;

$cos \ 65^(\circ) * 7=AC$

$0.423 * 7=AC$

$2.961=AC$

Rounding off to the nearest hundredth, we get;

$2.96=AC$

Thus, the length of AC is 2.96 units.

Jamie borrowed $361.75 from his uncle,who has agreed to charge him a monthly
simple interest rate of 2.5%. Jamie pays
his uncle back in 7 months.

Answers

He pays 370.28125.

What is Simple Interest?

Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Given:

Jamie borrowed = $361.75

Simple interest = 2.5%

As, Simple interest is not compounded.

so,

361.75 x 1.025

=370.28125

Hence, he pays 370.28125.

Learn more about simple interest here:

brainly.com/question/25845758

#SPJ2

Answer:

Jamie will pay back a total of 370.79

Step-by-step explanation:

361.75 x 1.025

Simple interest is not compounded so just multiply the borrowed amount by

1 + .025

Boatesville is a 65 3/5 -kilometer drive from stanton. A bus traveling from stanton to boatesville is 24 1/3 kilometers from boatesville. How far has the bus traveled

Answers

Answer:

41 4/15 is how far the bus has traveled

Step-by-step explanation:

total distance = distance traveled + distance to go

65 3/5 = x + 24 1/3

Subtract 24 1/3 from each side

65 3/5 - 24 1/3 = x

Get a common denominator of 15

65 3/5 *3/3 = 65 9/15

24 1/3 *5/5 = 24 5/15

65 9/15 - 24 5/15=x

41 4/15 is how far the bus has traveled

Sergio bought 1.2 pounds of turkey breast at the deli counter. He paid $8.34 for theturkey. What price per pound did he pay?

Answers

Answer:

.1438848921

Step-by-step explanation:

you divide 1.2 by 8.34 then multiply it by 8.34 to check

6.95 because you divide 8.34 by 1.2

For a statistics project a community college student at Diablo Valley College decides to investigate cheating in two popular majors at DVC: business and nursing. She selects a random sample of nursing and business courses and convinces the professors to distribute a short anonymous survey in their classes. The question about cheating is one of many other questions about college life. When the student summarizes the data, she finds that 42 of the 50 business students and 38 of the 70 nursing students admitted to cheating in their courses. Can the student proceed with the calculation of the confidence interval for the difference in population proportions?

Answers

Answer:

The student can proceed with the calculation of the confidence interval for the difference in population proportions. This is because, from the data she has, 3/4 of the Business students admitted to cheating while 1/2 of the Nursing students admitted to cheating also.

This is above the average number of students in her given sample size which is valid for extrapolation to the College Majors being investigated.

Step-by-step explanation:

Find the slope that goes through the ordered pairs (-4,8)(6,8)

Answers

1.level the point
2.slope formula to find the slope
3.substitute the slope(m) to y=mx+b
4.use one point (x,y) to solve for (b) y-int
5.substitute y-int (b) to y=mx+b
Then you are gonna get ur answer

Other Questions

A pump discharges 278 gallons of water in 3.5 minutes. How long would it take to empty a container with 750 gallons? Round up to the nearest minute

Image attached please help!A) which answer choices are trueB) which inequality is shown on the graph?

3 Which value of x satisfies the equation5(2x - 9) + 3 =-

What is the total interest paid on an $185,000 loan at 6.25% APR over 15 years (monthly payments)?