Question

mary buys a used car
use the information below to answer both 8.a and 8.b
mary buys a used car worth $11,000. each year the car depreciates at an annual rate of 10%. the value of the car can be represented by the function $f(t)=11,000(1 - 0.10)^t$, where $t$ is the number of years since the car was purchased
question 15.a
question 15.b
what is the y - intercept of the graph, and what does it mean in the context of the problem?
a. the y - intercept is (0, 11,000) and it represents the value of the car when mary bought it.
b. the y - intercept is (0, 11,000) and it represents the value of the car when mary sold it.
c. the y - intercept is (11,000, 0) and it represents the value of the car when mary bought it.
d. the y - intercept is (11,000, 0) and it represents the value of the car when mary sold it.

Explanation:

The y - intercept of a function \(y = f(t)\) is found by setting \(t = 0\). For the function \(f(t)=11000(1 - 0.10)^t\), when \(t = 0\), \(f(0)=11000(1 - 0.10)^0=11000\times1 = 11000\). In the context of the problem, \(t\) represents the number of years since the car was purchased. When \(t = 0\), it is the moment of purchase, and the value of the car is its initial purchase - price. The y - intercept is of the form \((0,y)\), so it is \((0,11000)\) and represents the value of the car when Mary bought it.

Answer:

A. The y - intercept is \((0, 11000)\) and it represents the value of the car when Mary bought it.