Question

You work at a restaurant and the head manager has sent you to purchase livestock for an experiment. You want to grow the meat for the food right at the restaurant. You have been given 500 gold coins to spend at the store to purchase the livestock. Each sheep costs 12 gold coins, while each chicken costs seven.

If you purchase 32 sheep, how many chickens can you buy? Show all of your work. Hint: you don’t have to spend every coin.

Write an inequality that represents this situation.

If you want to buy twice as many chickens as sheep, what is the maximum number of sheep you can buy? Show all of your work.

Make a graph of the inequality from #2. Remember to label all parts of the graph. Label the intercept points.

Part 2: The animals you bought for the restaurant are doing quite well. You purchased an initial flock of 30 sheep and 20 chickens. The chickens and sheep have been breeding very successfully, and the flocks are growing. The sheep breed at a rate so that they will double every year. The chickens breed faster than the sheep (it helps when you can lay multiple chicks from one hen at a time!) The population of the chickens multiplies by 2.2 each year. (For all of these problems round to the nearest animal.)

5. How many sheep will there be in five years? Show all of your work.

6. Create an exponential equation to represent this situation.

7. How many chickens will there be in eight years? Show all of your work.

8. Create an exponential equation to represent this situation.

9. During what year will there be more chickens than sheep? Show your work or explain how you know.

10. Plot the two curves on a graph together. Remember to label all parts of the graph.

11. What is the domain of each function?

12. What is the y-intercept for each function? Explain what this number means in the context of this situation.

13. Your field can support a maximum of 3000 animals before you run out of vegetation and space. During what year will you need to purchase more land to house the animals?

Answer 1

The number of chickens is 16 if you purchase 32 sheep and inequality is 12x + 7y ≤ 500.

What is an exponential function?

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent $\rm y = a^x$

where 'a' is a constant and a>1

Total coins = 500 gold coin

Each sheep costs 12 gold coins, while each chicken costs 7 gold coins.

If purchased 32 sheep, so the total cost for the 32 sheep:

= 32×12

= 384

Remaining gold coin = 500 - 384 = 116 gold coin

Number of chicken can purchase in 166 gold coin = 116/7 = 16.57 ≈ 16

Inequality for the above scenario:

Let x be the number of sheep and y be the number of chickens.

12x + 7y ≤ 500

If you want to buy twice as many chickens as sheep.

y = 2x

12x + 7y = 500

After solving both the equation:

x = 19.23 ≈ 19 (Number of sheep)

y = 38 (double the number of sheep)

For the part 2:

The exponential equation for the sheep:

$\rm y = 30(2)^x^-^1$

After 5 years, plug x = 5

$\rm y = 30(2)^4$

y = 480 sheep

The exponential equation for the chicken:

$\rm y = 20(2.2)^x^-^1$

After 8 years, plug x = 8

$\rm y = 20(2.2)^7$

y = 4988.71 ≈ 4988 chickens

Similarly, you can find the rest of the data using the above equation.

Thus, the number of chickens is 16 if you purchase 32 sheep and inequality is 12x + 7y ≤ 500.

Learn more about the exponential function here:

brainly.com/question/11487261

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