Chapter Test
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Use the general form of an exponential function, y=ab^x. Recall that b=1+r, where r is the rate of growth or decay.
Function: y=42 500 (1.03)^x
Graph:
To write the equation, we first need to define the variables. Let y be the annual salary, and let x be the number of years after the initial value. In this case, the initial value is an annual salary of $ 42 500. Since the salary increases by 3 % each year, we have that r=0.03. y=42 500 (1+ 0.03)^x ⇕ y=42 500 ( 1.03)^x To graph the function we will make a table of values. Since time is always greater than or equal to 0, we will assign non-negative values for x.
| x | 42500(1.03)^x | y=42500(1.03)^x |
|---|---|---|
| 42500(1.03)^() | 42500 | |
| 1 | 42500(1.03)^1 | 43775 |
| 3 | 42500(1.03)^3 | ≈ 46440 |
| 5 | 42500(1.03)^5 | ≈ 49269 |
| 9 | 42500(1.03)^9 | ≈ 55452 |
Let's now plot and connect the obtained points. Since both variables are non-negative, we will only draw in the first quadrant.
