Harry has a penny collection with 160 pennies. He plans to increase the size of his collection by a constant term each year for five years. This graph represents his goal for collecting over the next five years. Use the graph to answer the following questions.

A. After the second year, approximately how many pennies does Harry plan to have in his collection?

B. Approximately how many pennies does Harry plan to have in his collection at the end of his five-year plan?

C. By approximately what number does Harry plan to increase his collection over the five-year period?

D. According to his plan, approximately how many pennies will Harry add to his collection during the fourth year?

E. Halfway through the fourth year, Harry’s collection contains 400 pennies. Study the graph provided at the beginning of this activity. Find the point that represents his progress. What are the coordinates of the point?

F. Approximately how many more pennies will Harry need to add by the end of the fourth year to get back on plan?

Explanation:

The first thing I did was to write the numbers to the grid and add the points labeled with the letter of the question with which they are related.

See the graph attached.

Question A:

The y-coordinate of the green point labeled A is about half way between 300 and 400, i.e. 350.

Then, Harry plans to have approximately 350 pennies at the end of the second year

Question B:

The green point labeled B has coordinates (5, 1200), meaning that Harry plans to have approximately 1,200 pennies at the end of his five-year plan.

Question C:

Harry started his collection with approximately 150 coins. It is the y-coordinate (the value when x = 0): (200 - 100)/2 = 150.

Thus, Harry plans to increase his collection by approximately 1,200 - 150 = 1,050 pennies over the five-year period.

Question D:

The number of peenies that Harry will add to his collection during the fourth year, according to his plan, is the difference between the number of pennies at the end of the fourth year and the end of the third year.

The green point labeled D has coordinates (4, 800) meaning that his plan is to have approximately 800 pennies.

To find the number of pennies that Harry plans to have at the end of the third year  read the y-coordinate that meets the curve when x = 3. That is approximately (600 + 500) / 2 = 550.

The difference is 800 - 550 = 250 pennies.

Therefore, Harry will add approximately 250 pennies to his collenction d during the fourth year, according to his plan.

Question E:

The blue point labeled E shows the position on the grid of the 400 pennies halfway throuhg the fourth year.

The coordinates of this point is (3.5, 400).

Question F:

According to the plan, the number of pennies at the end of the fourth year would be 800 (green point labeled D on the graph).

Then, Harry will need to add approximately 800 - 400 = 400 pennies.

According to the plan the number of coins at the end of the third year would be

But the plan was to add 800 - 550 = 250.

Thus, Harry will need to add 400 - 250 = 150 more pennies than he had planned, during the fourth year.

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