a The general form of an exponential function is written in the following format.
f(x)=ab^x
In this equation, a is the initial value and b is the multiplier. From the exercise, we know that the purchasing price of the car was $12 250. We also know that the annual depreciation is 11 %. Annual is another word for yearly so time is in years. As for our function, we have an initial value of a= 12 250 and a multiplier of b= 0.89.
f(x)= 12 250( 0.89)^x
b The initial investment was $1000 and the annual interest is 6 %. This gives a starting value and multiplier of a= 1000 and b=1.06 respectively. Let's substitute this into the general form of an exponential function.
f(x)= 1000( 1.06)^x
However, the interest is compounded on a monthly basis. What this means is if the monthly interest rate is a, this value should,when multiplied twelve times, equal 1.06. We get the following equation.
a^(12)=1.06
Let's solve for a in this equation.
When the monthly multiplier is 1.0049, the annual appreciation will equal 1.06 when multiplied twelve times. With this information, we can rewrite the initial equation so that it reflects time in months.
f(x)=1000((1.0049)^(12))^x
⇕
f(x)=1000(1.0049)^(12x)
In this equation, x is measured in month.
