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What is the answer for question 10) ? http://postimg.org/image/5gm0wsol3/

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lkballer24 | Student, Grade 11 | (Level 1) Valedictorian

Posted May 23, 2013 at 10:33 PM via web

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What is the answer for question 10) ?

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violy | High School Teacher | (Level 3) Assistant Educator

Posted May 23, 2013 at 11:56 PM (Answer #1)

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The equation given is in the form V = a * b^y 

where a = original value of the car, b = rate of depreciation, and 

y number of years. 

So, for the first question rate of depreciation is 0.85 or 85%.

For the second question, we replace the y by 5. 

`V = 25000(0.85)^5 = 25000*0.4437053125 = $11092.63 `

` `Therefore, the value of the car after 5 years is $11.092.63.

For the last question, we will take the 10% of the original value.

`0.10 * 25000 = $2500`

So, our V = $2500, and we will solve for y.

`2500 = 25000(0.85)^y`

Divide both sides by 25000.

`0.10 = 0.85^y`

Take the natural logarithm of both sides.

`ln0.10 = ln0.85^y`

Use the property: lnu^v = vlnu on right side.

`ln0.10 = yln0.85`

Divide both sides by ln0.85.

`y = ln0.10/ln0.85 = 14.17 ` years or 14 years and 2 months.

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