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https://www-awu.aleks.com/alekscgi/x/Isl.exe/1o_u-IgNslkr7j8P3jH-DilwpxbwPrkicRI6pS60AVDIQYFU2WpWSCYgzO EXPONENTIAL AND LOGARITHMIC FUNCTIONSEvaluating an exponential function that models a real-world...The dollar value v(t) of a certain car model that is t years old is given by the following exponential functiev (t) = 27,500(0.78)Find the initial value of the car and the value after 10 years.Round your answers to the nearest dollar as necessary.Initial value:saValue after 10 years:saХ$?

Sagot :

V =$27500 Initial Value

V= 2292

1) Considering that equation

The initial value for that car is when it is brand new. At instant t=0, no depreciation so:

[tex]\begin{gathered} V(t)=27500(0.78)^t \\ \text{The initial value:} \\ V(0)=27500(0.78)^0\Rightarrow V(0)\text{ =27500} \end{gathered}[/tex]

As the property of exponents says that any number raised to zero, is equal to 1 then the car is worth V =$27500

b) The value after 10 years. Now after 10 yrs of devaluating that car:

[tex]\begin{gathered} V(t)=27500(0.78)^t \\ V(10)=27500(0.78)^{10} \\ V(10)\text{ =2292.33} \\ V(10)\cong2292 \end{gathered}[/tex]

All we have to do is to plug it into t the value of 10. After 10 years that

car is worth approximately $ 2292

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