A car sells for $5000 and loses (1)/(10) of its value each year. Write a function that gives the car's value, V(t),t years after it is sold. V(t)=

Identify Value and Depreciation Rate: Identify the initial value of the car and the rate at which it depreciates each year. The initial value of the car is $5000. The car loses 1/10 of its value each year, which means it depreciates by 10% annually.Write Depreciation as Decimal: Write the depreciation as a decimal to use in the function. Since the car loses 1/10 of its value each year, we convert this fraction to a decimal to get 0.1.Determine Depreciation Factor: Determine the depreciation factor for each year. To find the value of the car after each year, we subtract the depreciation rate from 1. This gives us the factor by which the car's value decreases each year. Depreciation factor = 1 - depreciation rate = 1 - 0.1 = 0.9Write Function for Car's Value: Write the function for the car's value after t years. The car's value after t years, V(t), can be represented by the initial value multiplied by the depreciation factor raised to the power of t. V(t) = Initial value * (Depreciation factor)^t V(t) = 5000 * (0.9)^t

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A car sells for
$5000 and loses
(1)/(10) of its value each year.
Write a function that gives the car's value,
V(t),t years after it is sold.

V(t)=

A car sells for $\$ 5000$ and loses $\frac{1}{10}$ of its value each year. $\newline$ Write a function that gives the car's value, $V(t), t$ years after it is sold. $\newline$ $V(t)= \square$

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Q. A car sells for

\$ 5000

and loses

\frac{1}{10}

of its value each year.

\newline

Write a function that gives the car's value,

V(t), t

years after it is sold.

\newline

V(t)= \square

Identify Value and Depreciation Rate: Identify the initial value of the car and the rate at which it depreciates each year. $\newline$ The initial value of the car is $\$5000$ . The car loses $\frac{1}{10}$ of its value each year, which means it depreciates by $10\%$ annually.
Write Depreciation as Decimal: Write the depreciation as a decimal to use in the function. $\newline$ Since the car loses $\frac{1}{10}$ of its value each year, we convert this fraction to a decimal to get $0.1$ .
Determine Depreciation Factor: Determine the depreciation factor for each year. $\newline$ To find the value of the car after each year, we subtract the depreciation rate from $1$ . This gives us the factor by which the car's value decreases each year. $\newline$ Depreciation factor = $1 - \text{depreciation rate} = 1 - 0.1 = 0.9$
Write Function for Car's Value: Write the function for the car's value after $t$ years. $\newline$ The car's value after $t$ years, $V(t)$ , can be represented by the initial value multiplied by the depreciation factor raised to the power of $t$ . $\newline$ $V(t) = \text{Initial value} \times (\text{Depreciation factor})^t$ $\newline$ $V(t) = 5000 \times (0.9)^t$