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Salsk061 [2.6K]
3 years ago
13

The equation A(t) = 900(0.85)t represents the value of a motor scooter t years after it was purchased. Which statements are also

true of this situation?

Mathematics
1 answer:
ValentinkaMS [17]3 years ago
8 0

Answer:

When new, the scooter cost $900

Step-by-step explanation:

<u><em>The complete question in the attached figure</em></u>

we have

A(t)=900(0.85)^t

This is a exponential function of the form

A(t)=a(b)^t

where

A(t) ----> represent the value of a motor scooter

t ----> the number of years after it was purchased

a ---> represent the initial value or y-intercept

b is the base of the exponential function

r is the percent rate of change

b=(1+r)

In this problem we have

a=\$900\\b=0.85

The base b is less than 1

That means ----> is a exponential decay function (is a decreasing function)

Find the percent rate of change

b=(1+r)\\0.85=1+r\\r=0.85-1\\r=-0.15

Convert to percentage (multiply by 100)

r=-15\% ---> negative means is a decreasing function

<u><em>Verify each statements</em></u>

<em>case A</em>) When new, the scooter cost $765.

The statement is false

Because the original value of the scooter was $900

case B) When new, the scooter cost $900

The statement is true (see the explanation)

case C) The scooter’s value is decreasing at a rate of 85%  each year

The statement is false

Because the scooter’s value is decreasing at a rate of 15%  each year (see the explanation)

case D) The scooter’s value is decreasing at a rate of  0.15% each year

The statement is false

Because the scooter’s value is decreasing at a rate of 15%  each year (see the explanation)

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