MATHEMATICS MIDDLE SCHOOL

Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equation 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.1 year
2 years
5 years
8 years

Answers

Answer 1

Answer:

9514 1404 393

Answer:

Step-by-step explanation:

A graphing calculator shows the function ...

f(t) = 16000(1 -0.35)^t -2000

will be zero for t ≈ 4.83 years. Rounded to the nearest year, the value is expected to be about $2000 after 5 years.

Using a scientific calculator, you can rewrite the equation to make use of logarithms.

2000 = 16000(1 -0.35)^t

2000/16000 = 0.65^t

log(1/8) = t·log(0.65)

t = log(0.125)/log(0.65) ≈ 4.827

Devon's car will be about 5 years old when its value is $2000.

_____

Additional comment

We expected to see the same sort of formula for continuous depreciation that we see for continuous growth: 2000 = 16000e^(-rt). The value formula given in the problem statement is a continuous function, but it should not be described as modeling continuous depreciation.

Answer 2

Answer:

Answer:

Step-by-step explanation:

Correct on EDGE 2022

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why do whole numbers raised to an exponent get greater while fractions raised to an exponent get smaller?

Answers

Any number above 1 gets greater, below 1 smaller (when above 0), while 1 itself remains the same. Negative numbers are more unpredictable.

Answer:

Because whole numbers are greater than 1 and any number greater than 1 multiplied by it self several times result in a greater number, but proper fractions are numbers less than 1, and a number less than 1 multiplied by it self several times result if a smaller number.

Explanation:

Whole numbers areraised to an exponent , means that such number is multiplied by itself (as many times and the exponent is).

Whole numbers are 1, 2, 3, 4, ....

Number 1 is a special case. When 1 is multiplied by it self the result is 1.

When other whole number (2, 3, 4, 5, ...) is multiplied by it self the result is a greater number. For example, 2 × 2 = 4, 3 × 3 = 9, and so on.

On the other hand, proper fractions, which are those whose numerator is less than the denominator, are less than one, and any number less than 1 multiplied by it self results in a smaller number.

For example: 1/2 × 1/2 = 1/4 or 0.5 × 0.5 = 0.25. This is always true for any proper fraction (a number less than 1).

What is the equation of the line that has slope -4 and passes through the point (-2,-5)

Answers

Answer:

y+5==4(x+2) this is point slope form

Step-by-step explanation:

Round to the place value of 4 in 934567

Answers

93500 would be the answer.

:)

Daniel worked for 213213 hours and earned $18.20. How much would he make if he worked for 514514 hours? Enter your answer in the box.

Answers

convert the hours to improper fractions

2 and 1/3 hours=2+1/3=6/3+1/3=7/3
5 and 1/4=5+1/4=20/4+1/4=21/4

ratio and proprtion
time/pay=(7/3)/18.2
if work 21/4 hours how much is pay
(7/3)/18.2=(21/4)/pay
times both sides by 18.2pay aka cross multiply
(7/3)pay=(21/4)18.2
(7/3)pay=382.2/4
times both sides by (3/7) to clear fraction (7/3 times 3/7=21/21=1)
pay=1146.6/28
pay=40.95

will earn $40.95 in 5 and 1/4 hours

Which one is bigger 2/3 or 4/7