Two sides of a triangle are 8 inches and 12 inches long each

The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price

likoan [24]

Answer:

A) 3%

B) Product A

Step-by-step explanation:

Exponential Function

General form of an exponential function: $y=ab^x$

where:

a is the initial value (y-intercept)
b is the base (growth/decay factor) in decimal form
x is the independent variable
y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Part A

Product A

Assuming the function for Product A is exponential:

$f(x) = 0.69(1.03)^x$

The base (b) is 1.03. As b > 1 then it is an increasing function.

To calculate the percentage increase/decrease, subtract 1 from the base:

⇒ 1.03 - 1 = 0.03 = 3%

Therefore, product A is increasing by 3% each year.

Part B

$\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100$

To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:

$\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%$

Check using different two consecutive values of f(t):

$\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%$

Therefore, as 3% > 1%, Product A recorded a greater percentage change in price over the previous year.

Although the question has not asked, we can use the given information to easily create an exponential function for Product B.

Given:

a = 10,100
b = 1.01
n = t - 1 (as the initial value is for t = 1 not t = 0)

$\implies f(t) = 10100(1.01)^{t-1}$

To check this, substitute the values of t for 1 through 4 into the found function:

$\implies f(1) = 10100(1.01)^{1-1}=10100$

$\implies f(2) = 10100(1.01)^{2-1}=10201$

$\implies f(3) = 10100(1.01)^{3-1}=10303.01$

$\implies f(4) = 10100(1.01)^{4-1}=10406.04$

As these values match the values in the given table, this confirms that the found function for Product B is correct and that Product B increases by 1% per year.

4 0

2 years ago

What’s the answer to this question?

nordsb [41]

Answer:

c

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

What is the perimeter of the rectangle?

UkoKoshka [18]

B. Because 5 t 5 t 4 t 4 equals 18

6 0

3 years ago

Read 2 more answers

Assume that in October of a particular year about 215 billion text messages were sent or received in the US, and the prediction

Julli [10]

Answer:

There will be $243$ billion messages sent or received in November.

Step-by-step explanation:

Given.

Number of text messages sent or received $=215$ billion.

Increment on the very next month $=13\%=\frac{13}{100}=0.13$

Lets find what is $13\%\ of\ 215$

⇒ $13\%\ of\ 215$

⇒ $0.13\times 215=27.95$

So we will add this value to our previous months data.

Now

Number of text messages sent in the month of November $=(27.5+215)=242.95$ billion.

Rounding to the nearest tenth the answer will be $243$ billion.

So $243$ billion text messages were sent or received in November.

5 0

3 years ago

The library is located 1.8 miles west of Callie’s house. The grocery store is located 2.4 miles south of the library. What is th

Verizon [17]

____________________________________________________

Answer:

Your answer would be 3 miles.

____________________________________________________

Explanation and work:

To find the answer for this question, we would use the numbers we know that was provided in the question and use it to get us the answer.

The equation we would use in this type of question is the Pythagorean Theorem.

Pythagorean Theorem:

a² + b² = c²

When you draw out the different locations, it would end up looking like a triangle since you trying to find the diagonal line from the grocery store to the house. In the triangle, it would be the hypotenuse. I will put a picture below.

Lets start solving:

1.8 would be plugged into "a"

2.4 will be plugged into "b"

(1.8)² + (2.4)² = c²

↓ ↓ ↓

3.24 + 5.76 = c²

↓

9 = c²

↓

√9 = √c²

↓

3 = c

3 miles would be your FINAL answer.

____________________________________________________

4 0

3 years ago