Use the vertical line test to determine whether the relation graphed is a function.

HELPPPP 100 points if you help!!!!

nignag [31]

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 a is the initial population and r is the rate of change.

We will substitute 15 for a and 1.12 for r. Hence:

$c(t)=15(1.12)^t$

This represents the number of people in the chorus after t 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 t 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 t. So:

$15(1.12)^t=2t+30$

Unfortunately, it is impossible to solve for t 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.

5 0

2 years ago

PLS HELP 9,10,11!!! ASAP

taurus [48]

Answer:

idk hff 8gciy ctcs 6rxtc igv6rx8

7 0

2 years ago

PLEASE PLEASEE ANSWER THE QUESTION IN THE PICTURE BELOW

KatRina [158]

Answer: Choice C

Vertex = (5, -2)

===============================================

Explanation:

Vertex form is $y = a(x-h)^2 + k$ where the vertex itself is located at (h,k)

As the name implies, we can very quickly pull out the coordinates of the vertex without doing much math at all.

In the case of choice C, we have $y= \frac{1}{2}(x-5)^2 - 2$ which is the same as $y = \frac{1}{2}(x-5)^2 + (-2)$ and we can see that h = 5 and k = -2. Therefore, the vertex is located at (h,k) = (5, -2)

8 0

2 years ago

I need in depth help answering

Volgvan

What is the question

8 0

2 years ago

This number is in scientific notation. 2. 4 × 10-4 Convert the number into standard notation. What is the value? 2. 4 × 10-4 =.

dusya [7]

The value of the number 2.4x10⁻⁴ in the standard notation is 0.00024.

<h3>What are Scientific notations?</h3>

The way through which a very small or a very large number can be written in shorthand. In scientific notations when a number between 1 and 10s is multiplied by a power of 10.

For example, 6,500,000,000,000 can be written as 6.5×10¹².

As the value of the scientific notation is given 2.4x10⁻⁴, therefore, for bringing it in the standard form we need to shift the decimal to the left by four digits. So,

$2.4 \times 10^{-4}\\\\= \dfrac{2.4}{10000}\\\\= 0.00024$

Hence, the value of the number 2.4x10⁻⁴ in the standard notation is 0.00024.

Learn more about Scientific notation:

brainly.com/question/1740231

5 0

1 year ago