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
Mamont248 [21]
3 years ago
5

HELPPPP 100 points if you help!!!!

Mathematics
1 answer:
nignag [31]3 years ago
5 0

Answer:

Part A)

Chorus:

c(t)=15(1.12)^t

Band:

b(t)=2t+30

Part B)

After 9 years:

The chorus will have about 41 people.

And the band will have 48 people.

Part C)

About approximately 11 years.

Step-by-step explanation:

We are given that there are 15 people in the chorus. Each year, number of people in the chorus increases by 12%. So, the chorus increases exponentially.

There are 30 people in the band. Each year, 2 new people join the band. So, the band increases linearly.

Part A)

Since after each year, the number of people in the chorus increases by 12%, the new population will be 112% or 1.12 of the previous population.

So, using the standard form for exponential growth:

c(t)=a(r)^t

Where <em>a</em> is the initial population and <em>r</em> is the rate of change.

We will substitute 15 for <em>a </em>and 1.12 for <em>r</em>. Hence:

c(t)=15(1.12)^t

This represents the number of people in the chorus after <em>t</em> years.

We are given that 2 new people join the band each year. So, it increases linearly.

Since there are already 30 people in the band, our initial point or y-intercept is 30.

And since 2 new people join every year, our slope is 2. Then by the slope-intercept form:

b(t)=mt+b

And by substitution:

b(t)=2t+30

This represents the number of people in the band after <em>t</em> years.

Part B)

We want to find the number of people in the chorus and the band after 9 years.

Using the chorus function, we see that:

c(9)=15(1.12)^9\approx41.59\approx41

There will be approximately 41 people in the chorus after 9 years.

And using the band function, we see that:

b(9)=2(9)+30=48

There will be 48 people in the band after 9 years.

Part C)

We want to determine after approximately how many years will the number of people in the chorus and band be equivalent. Hence, we will set the two functions equal to each other and solve for <em>t</em>. So:

15(1.12)^t=2t+30

Unfortunately, it is impossible to solve for <em>t</em> using normal analytic methods. Hence, we can graph them. Recall that graphically, our equation is the same as saying at what point will our two functions intersect.

Referring to the graph below, we can see that the point of intersection is at approximately (10.95, 51.91).

Hence, after approximately 11 years, both the chorus and the band will have approximately 52 people.

You might be interested in
45+ 46+47+ 48+ ... 113 + 114Gauss approach
Doss [256]

Answer:

5565

Step-by-step explanation:

1+2+3+4...+113+114=\frac{114*115}{2} =6555

1+2+3+4 ... +43+44=\frac{44*45}{2} =990

Thus, 45+46+47+48...+113+114= 6555-990=5565

3 0
3 years ago
The greatest number that divide 60 and 84 without leaving a reminder ​
a_sh-v [17]

Step-by-step explanation:

HCF of 60 and 84 = 6

So the required greatest number that divides 60 and 84 without leaving remainder is 6.

6 0
3 years ago
Read 2 more answers
The diameter of a circle is 28 inches what is the circle's area?<br><br> use 3.14 for pi
jolli1 [7]

Answer:

615.75216....

Step-by-step explanation:

The formula is A = π * (ø/ 2)^2

A = Circle area

π = Pi = 3.14

ø = Circle diameter

A= 3.14  (28/2)^2

5 0
3 years ago
Read 2 more answers
Giving brainliest! View image!
Tatiana [17]

Answer:

58%

Step-by-step explanation:

10*5=50

7*3=21

21/50 chance to choose inside small rectangle

21/50*2 = 42/100 chance to choose inside small rectangle

100-42=58%

3 0
2 years ago
A factor other than the independent variable that might produce an effect in an experiment is called a
Varvara68 [4.7K]
The answer is Confounding Variable
8 0
3 years ago
Other questions:
  • What is 4 pi cubed divided by 3
    14·1 answer
  • Dan invests £1300 into his bank account.
    15·1 answer
  • The basic ratio for 24:56
    9·2 answers
  • Convert 5.70 lbs to grams and explain please help
    6·1 answer
  • Please help me solve
    11·1 answer
  • What is the slope of the line? Thank youu
    14·1 answer
  • Question 3<br> Name the transformations of the next equation y
    15·1 answer
  • A student simplified the expression 6^2/12^2 as 1/2 do you agree
    7·1 answer
  • 50 POINTS+BRAINLIEST!!!!
    12·2 answers
  • 1. How much does the glass for region 1 cost?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!