Answer:
Function for given situation is : [tex]V(t)=3000(0.70)^t[/tex]
Value of computer after 4 years = $720.3.
Step-by-step explanation:
Given that the value of a $3000 computer decreases about 30% each year. Now we need to write a function for the computers value V(t). then we need to find about how much will the computer be worth in 4 years.
It clearly says that value decreases so that means function represents decay.
For decay we use formula:
[tex]A=P(1-r)^t[/tex]
where P=initial value = $3000,
r= rate of decrease =30% = 0.30
t= number of years
A=V(t) = future value
so the required function is [tex]V(t)=3000(1-0.30)^t[/tex]
or [tex]V(t)=3000(0.70)^t[/tex]
Now plug t=4 years to get the value of computer after 4 years.
[tex]V(4)=3000(0.70)^4[/tex]
[tex]V(4)=720.3[/tex]
Hence final answer is $720.3.
