4.2.1: Preparation 4.2

(1) In Exercise 3.4, you used a model to determine the amount owed on a loan of $5,000 with simple interest of 4.25%. The model was A = 5000 + 5000(0.0425t), where A is the amount (total principal plus interest) required to repay a loan, and t is the time, in years.

(a) What is the slope of this model? Include units in your answer. (Hint: Think about simplifying the equation or use the equation to find a few values and see how much the amount increases each year.)

(b) In Exercise 3.4, you estimated how long it would take for the loan amount to reach $7,000. Now, instead of estimating it, use the given model to find it. Round your answer to the nearest tenth. Be sure to show your work.

(2) Ali wants to save money to buy a new video game. Ali’s mother agrees to help him by paying him for each “A” he receives on a test in school. Ali’s mother creates a spreadsheet to show Ali how much money he will have based on the number of tests on which he earns an “A.” The spreadsheet with the formula is shown below.

Indicate if each statement is true or false.

(a) Ali did not have any money saved to begin with.

(i) True

(ii) False

(b) Ali will receive $1.50 for each “A” he earns.

(i) True

(ii) False

(c) The slope of this model is $1.50/test with a grade of “A.”

(i) True

(ii) False

(d) The vertical intercept of this model is $1.50.

(i) True

(ii) False

(e) The horizontal intercept of this model is $1.50.

(i) True

(ii) False

(f) If Ali’s grandfather offers to add $0.50 to the amount Ali gets for each test, the slope of the model would increase.

(i) True

(ii) False

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