Answer:
[tex]v=800(0.75)^t[/tex]
$189.84 (nearest cent)
Step-by-step explanation:
If a computer loses 1/4 of its value each year, then each year it will be 75% of the value of the previous year, since 100% - 25% = 75%.
Therefore, we need to model this as an exponential function.
General form of an exponential function: [tex]y=ab^x[/tex]
where:
- a is the y-intercept (or initial value)
- b is the base (or growth factor) in decimal form
- x is the independent variable
- y is the dependent variable
From the given information:
- a = $800
- b = 75% = 0.75
- x = t
- y = v
Substituting the values into the formula:
[tex]\implies v=800(0.75)^t[/tex]
When x = 5, t = 5
[tex]\implies v=800(0.75)^5=189.84375[/tex]
⇒ v = $189.84 (nearest cent)
