Answer:
Step-by-step explanation:
The standard form for an exponential equation is
We have 2 unknowns, a and b, but that's all good because we have 2 (x, y) coordinates we can utilize in order to find a and b. In our coordinate pair, x is the number of years gone by and y is the value after that number of years. The problem tells us that an item was purchased for $500. That translates to "before any time has gone by, the initial value of the item is $500". In other words, with x being time, no time has gone by, so x = 0. When x = 0, y = 500. (0, 500). Do the same for the next set of numbers. When x = 2 years gone by, the value is $551.25, so the coordinate is (2, 551.25). Now we use them to find a. Use the first coordinate:
Anything raised to the 0 power = 1, therefore:
and a = 500.
Now onto the next coordinate point using the a value we just found:
Divide both sides by 500 to get
so b = 1.05.
Now we have the values for a and b, so we fill in: