Question

A boat's value over time is given as the function f(x) and graphed below. Use A(x) = 400(b)x + 0 as the parent function. Which graph shows the boat's value increasing at a rate of 25% per year?

Answer 1

Answer:

Last Graph (4th one)

Step-by-step explanation:

The equation given is  $A(x)=400*b^x + 0\\A(x) = 400b^x$

Since we want increase of 25%, the value of b would be 1.25, so we have:

$A(x)=400(1.25)^x$

The graph should be increasing so we can immediately eliminate 2nd and 3rd graphs since they are clearly decreasing. We now have to choose between 1st graph and 4th graph.

1st graph:

Let's take the point (-20,30)

$A(x)=400(1.25)^{-20}\\A(x)=4.65$

2nd graph:

Let's take the point (-20,4.5)

$A(x)=400(1.25)^{-20}\\A(x)=4.65$

hence, this makes sense. So the correct graph is 4th one.