Linear vs. ExponentialReal World Applications

Warm Up: System of Equations Warm Up

Homework Questions:

Review:

Do you know what type of function is given in this table?

The difference in y-values is always two, a constant.The graph is linear and is verified at right.

Review:

Do you know what type of function is given in this table?

The first difference in y-values is not constant but the second difference is. The graph is quadratic and is verified at right.

Review:

Do you know what type of function is given in this table?

The difference in y-values follows a pattern similar to the y-values. The graph is exponential and is verified at right because you multiply by 2 each time.

COMPARING LINEAR VS. EXPONENTIAL

Mrs. Tran wants to put $$ in the bank for saving. She have two choices for her saving. Choice 1: She can put $10 in her bank and each week put an additional $2. Choice 2: She can put $1 in her piggy and double each week. When will the amount of money she put in her piggy from choice 2 exceed her choice 1?

Choice 1 vs. Choice 2 in equation form:

Let’s look at it in a table perspective:

Let’s graph them. What does the point of intersection mean?

Let’s Try another:

• Mr. Smith has an apple orchard. He hired his daughter, Lucy, to pick up the apples and offered her two payments option:

• Option A: $1.50 per bushel of apples picked• Option B: 1 cent for picking one bushel, 3 cent for

picking 2 bushel, 9 cent for picking 3 bushel, and so on with the amount being triple for each additional apple bushel picked.

Write a function to model each option

If Lucy pick 6 bushel which option should she picked?

If Lucy picked 12 bushel which option should she picked?

How many bushel would Lucy have to pick to make option B better than option A?

Let’s Try Again

• Ben has $100 in his savings account. He wants to save more money. He is looking at two investment plans. Under plan A, he will increase his account balance by $20 a year. Under plan B, he will increase his account balance by 15% each year. How much more will he save with Plan B after 10 years?

Plan A vs. Plan B in equation form:

Let’s look at it in a table perspective:

Let’s graph them. What does the point of intersection mean?

Any Questions

Quiz Time