Question

a building is depreciating at a rate of 3% per year. julio wants to create a graph that represents the value of the building that was originally worth $75,000. he will use the following equation: $v = 75,000(0.97)^t$ which statements are true about the graph? select all that apply. a. the graph is exponentially decreasing. b. v is the value of the building after t years. c. the y-intercept is 75,000. d. the graph is exponentially increasing. e. t is the value of the building after v years.

Explanation:

• For option A: The equation is in the form $v = a(b)^t$ where $0 < b < 1$ ($b=0.97$), so it is an exponentially decreasing function.
• For option B: By definition of the given equation, $v$ represents the building's value after $t$ years.
• For option C: The y-intercept occurs when $t=0$. Substitute $t=0$: $v=75000(0.97)^0=75000(1)=75000$.
• For option D: Since $b=0.97 < 1$, the function decreases, not increases.
• For option E: $t$ represents time in years, not the value of the building; $v$ is the value.

Answer:

A. The graph is exponentially decreasing.
B. v is the value of the building after t years.
C. The y-intercept is 75,000.