Learning Resources

Investigation 2: Relationships & Focus B: Exponential Functions

Test yourself (solution)

1 (a) Interest earned first year = 8% of $500 = $40
Value of investment when Marcie is 1 yr old = $500 + $40 = $540
Alternately, we can multiply initial amount by 1.08 to get 1.08 x $500 = $540
Similarly, value when Marcie is 2 = 1.08 x $540 = $583.20
Continue this process and put answers in a table form.

age 0 1 2 3 4 5 6 7
value $500 $540 $583.20 $629.85 $680.24 $734.66 $793.44 $856.91

(b) The table represents an exponential function because the ratio of successive terms is constant, viz.1.08 (check the ratio of any two successive values to assure yourself of this). It is a growth function because the values of the dependent variable (value of the investment) increases as the values of the independent variable (Marcie's age) increases.

(c) We could complete the table till we reach the age of 21. However, the function that defines the table is y = 500 x 1.08^x , where y is the value and x is Marcie's age. At age 21 we thus have:

y = 500 x 1.08²¹ = $2516.92

(d) To figure out how long she will have to wait before the investment is $5000, we have to think in reverse. Let y = 5000 in the equation and find x. We have to solve :

5000 = 500 x 1.08^x or 10 = 1.08^x (dividing through by 500)
rewriting the equation to equal 0 we get: 0 = 1.08^x - 10

Using the [SOLVER] function on the TI83 as shown in the lesson we get:

When she is 30 years old the investment will be at least $5000. (As an extra to this problem, it is left to you to figure out exactly how much it will be on her 30 birthday)