Celeste deposited $10,000 into a savings account that pays 2.8% compounded monthly. The equation below represents the amount of money, A, Celeste will have in t years.

the formula A equals 10000 times the quantity 1 + .028/12) raised to the 12t

Celeste wants to know how many years will it take her to earn $1,000 in interest.

Step 1: Enter equation into [Y=].
Step 2: Since Y represents the amount of money in her account, enter the amount Celeste will have when she earns $1000 into Y2. (That amount will be the original deposit of $10,000 plus the $1,000 in interest.)

graphing calculator screen showing Y1 equals 10000 times the quantity 1 + .028/12) raised to the 12X and Y2 equals 11000

Step 3:

[Window] Reset window to fit domain and range for this problem situation.

What would be a reasonable domain and range for this problem? Explain.

Interactive popup. Assistance may be required.

Check Your Answer.

X min = 0 The minimum number of years that money can be invested is 0.
X max = 6 This is only an educated guess. We do not know how many years it will take to earn $1000.
Y min = 10000 This is the minimum amount of money that will be in the account.
Y max = 12000 Choose any number greater than 11000 since this is the amount of money she will need in her account to have earned $1000.

graphing calculator screen showing the intersection of two curves Close Pop Up

 

Step 4:[GRAPH] If the intersection of the two functions is not visible, readjust your window by changing the X max.

graphing calculator screen showing the CALCULATE menu with intersect indicated

Step 5: To view CALCULATE menu, choose [2nd][TRACE]

Step 6: To find intersection, choose 5:intersect.

Step 7: When the question "First Curve?" appears on the screen make sure your cursor is on one of the curves and Press [ENTER]. The question "Second curve?" should appear. Check to be sure your cursor is on the other curve. Press [ENTER]. The question "Guess?" should appear. Move your cursor close to the intersection you are trying to find and Press [ENTER].

graphing calculator screen showing the intersection of two curves with the question “First Curve” at the bottom of the screen

What does this intersection mean?

graphing calculator screen showing the Intersection of two curves with x=3.4079047 and y = 11000

In your notes, compare the table method and the graphing method for solving exponential equations.