0 and 0decay factor. The decay factor can be also written as 1-r, where r is the percent rate of change expressed as a decimal. Therefore, we can write the exponential decay function as'>
y=a* b^x
Here, a>0 and 0decay factor. The decay factor can be also written as 1-r, where r is the percent rate of change expressed as a decimal. Therefore, we can write the exponential decay function as shown below.
y=a* (1-r)^x
Finally, let's take a look at the given function, which models the car's value after x years.
y=30 000(0.85)^x
We can see that the decay factor is equal to 0.85. As we have mentioned before, it can be rewritten in the form 1-r.
0.85=1-0.15
Therefore, the car's value depreciates by 15 % each year.
b Let's take a look at the given function.
y=30 000(0.85)^x
Here y describes the car's value after x years. To find out what the value of the car will be in 1 year we have to substitute 1 for x. Let's do it!
After one year the car will be worth about $25 500.
c Let's take a look at the given function.
y=30 000(0.85)^x
Here y describes the car's value after x years. To find out what the value of the car will be in 4 years we have to substitute 4 for x. Let's do it!
