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Furkat [3]
1 year ago
14

Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equ

ation 2,000 = 16,000(1-r) t represents the situation, where t is the age of the car in years and r is the rate of depreciation. About how old is Devon’s car? Use a calculator and round your answer to the nearest whole number.
Mathematics
1 answer:
77julia77 [94]1 year ago
5 0

Answer:

Step-by-step explanation:

Use the equation 2,000 = 16,000(1-r)^t to solve for t;

2000 = 16000(1-0.35)^t

Divide both sides by 16000

2000/16000 = 0.65^t

0.125 =0.65^t

Introduce logarithm on both sides;

<em>ln</em> 0.125 = t <em>ln</em> 0.65

Divide both sides by <em>ln</em> 0.65;

(<em>ln</em> 0.125) / (<em>ln</em> 0.65) = t

-2.07944/ -0.4308 = t

4.827 = t

t= 5 (as a whole number)

Therefore, the car is about 5 years old.

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To solve this problem, we must first convert all of the numbers represented by words into their numeral equivalents so we can simplify. To do this, we must remember that the ones place is the first to the left of the decimal point, and the tens place is one place farther to the left. If we have 4 tens and 3 ones, this is the same as 43 (we put the digit 4 in the tens place and the digit 3 in the ones place). If we replace our words with our new numerical value, we get:

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To solve this, we just multiply these two numbers together, which gives us:

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Hope this helps!

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