Check if the constant multiplier is greater than one or not.
About 9 years
Practice makes perfect
We will first find the function that models the situation. To find the answer, we will use two methods.
Use a table
Use a graph
Finding the Function
We know that an investment of $100 is expected to grow 8 % each year. The growth of the investment can be modeled by an exponential growth function.
I(t)= a* (1+ r)^t
Here, a is the principal and r is the percent rate of change. With the function, we can find the value I(t) of our investment after t years. Since the principal is $ 100 and the percent rate of change is 8 %, we can write the function.
I(t)= 100* (1+ 0.08)^t ⇔ I(t)=100* (1.08)^t
Using a Table
We want to find when the investment doubles itself. To find it, we will make a table of the function I(t)=100* (1.08)^t. When we find a value greater than 200, two times the principal, we will stop.
t
100* (1.08)^t
I(t)=100* (1.08)^t
0
100* (1.08)^0
100
3
100* (1.08)^3
≈ 126
6
100* (1.08)^6
≈ 159
9
100* (1.08)^9
≈ 200
12
100* (1.08)^(12)
≈ 252
We see that when t=9, the value of the investment is about 200. Hence, it takes approximately 9 years for the investment to double.
Using a Graph
We can also find the approximate amount of time by using the graph of the function. When the investment is doubled, it will be $200. Therefore, we need to draw the line I(t)=200 as well as the graph of the function.
We see that the graphs intersect at about t=9. Therefore, the approximate amount of time is 9 years.
Showing Our Work
Drawing the graph of the function
We can use the points we found in the table above. Let's plot and connect the points ( 0,100), ( 3,126), ( 6,159), ( 9,200), and ( 12,252) with a smooth curve.
