Type the correct answer in each box. Use numerals instead of words.

Two chain restaurant brands, Joey's Refuge and Kane's Deli, were founded in the same year, although some outlets of Kane's Deli were operating under a different name before Kane's Deli was founded.
The owner of Joey's Refuge uses the equation below to represent the number of restaurants, y, he owns x years after the brand's founding.

y=2^x

The owner of Kane's Deli uses the equation below to represent the number of restaurants, y, he owns x years after the original brand's founding.

y=4x+12

Use graphing technology, and complete the given statements.

After (fill in the blank) years, Joey's Refuge and Kane's Deli will own the same number of restaurants. At that time, each chain will own (fill in the blank) restaurants.

The intersection point of the two graphs represents the point where the chains own the same number of restaurants. The coordinates of this point are (5, 32).

The x-value is the number of years; this is 5.

The y-value is the number of restaurants; this is 32.

Answer Link

Tutorconsortium307 Tutorconsortium307 · Answer 2 · 2022-06-17T20:51:09+02:00

After 5 years, Joey's Refuge and Kane's Deli will own the same number of restaurants. At that time, each chain will own 32 restaurants. This can be obtained by putting values for x and finding corresponding values of y and plotting the graph.

Calculate the coordinates of graph:

Given the first equation, y = 2ˣ

Putting values for x to find corresponding y,

When x = 0, y = 2⁰ = 1 ⇒ A(0,1)

When x = 1, y = 2¹ = 2 ⇒ B(1,2)

When x = 2, y = 2² = 4 ⇒ C(2,4)

When x = 3, y = 2³ = 8 ⇒ D(3,8)

Now plot the points A(0,1), B(1,2), C(2,4), D(3,8) on the graph. Join the points.

Similarly,

Given the first equation, y = 4x+12

Putting values for x to find corresponding y,

When x = 0, y = 4(0) + 12 = 12 ⇒ A(0,12)

When x = 1, y = 4(1) + 12 = 16 ⇒ B(1,16)

When x = 2, y = 4(2) + 12 = 20 ⇒ C(2,20)

When x = 3, y = 4(3) + 12 = 24⇒ D(3,24)

Now plot the points A(0,12), B(1,16), C(2,20), D(3,24) on the graph. Join the points.

By observing the graph we see that the intersecting point is (5,32).

Hence we can say that after 5 years, Joey's Refuge and Kane's Deli will own the same number of restaurants and each chain will own 32 restaurants.

Learn more about plotting a graph here:

brainly.com/question/13432896

#SPJ2