02.10.2020

Rich is comparing the cost of maintaining his car with the depreciation value of the car. The value starts at $20,000 and decreases by 15% each year. The maintanance cost is $500 the first year and increases by 28% per year. When will the maintenance cost and the value be the same.

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Mathematics

Rich is comparing the cost of maintaining his car with the depreciation value of the car. The value starts at $20,000 and decreases by 15% each year. The maintanance cost is $500 the first year and increases by 28% per year. When will the maintenance cost and the value be the same. Please explain step by step

Step-by-step answer

P Answered by Specialist

The maintance cost and the value will be the same in 9 years.

Step-by-step explanation:

Exponential function:

An exponential function has the following format:

y(t) = y(0)(1 + r)^t

In which r is the rate of change.

The value starts at $20,000 and decreases by 15% each year.

This means that V(0) = 20000, r = -0.15

V(t) = V(0)(1 + r)^t

V(t) = 20000(1 - 0.15)^t

V(t) = 20000(0.85)^t

The maintance cost is $500 the first year and increases by 28% per year.

This means that M(0) = 500, r = 0.28 . So

M(t) = M(0)(1 + r)^t

M(t) = 500(1 + 0.28)^t

M(t) = 500(1.28)^t

When will the maintenance cost and the value be the same.

This is t for which:

V(t) = M(t)

20000(0.85)^t = 500(1.28)^t

$\frac{(1.28)^t}{(0.85)^t} = \frac{20000}{500}$

$(\frac{1.28}{0.85})^t = 40$

$\log{(\frac{1.28}{0.85})^t} = \log{40}$

$t\log{(\frac{1.28}{0.85})} = \log{40}$

$t = \frac{\log{40}}{\log{(\frac{1.28}{0.85})}}$

t = 9

The maintance cost and the value will be the same in 9 years.

Mathematics

Anthony received $150 for his birthday this year. This was $10 less than half the amount he received last year. How much money did Anthony receive for his birthday last year?

Step-by-step answer

P Answered by PhD

The answer is in the image

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A new school randomly assigns a six-character student code to every prospective student. The school uses the characters 1, 2, 3, 4, 5, X, Y, and Z. If none of the student codes contain a repeated character, what is the total number of codes that can be randomly assigned?

Step-by-step answer

P Answered by PhD

The total nom of code that can be used is equal to 5+3 = 8

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In a parking lot, for every 8 cars there are 7 trucks. What is the ratio of cars to trucks? A)7 : 8 B)8 : 7 C)8 : 15 D)15 : 8

Step-by-step answer

P Answered by PhD

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

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Which number is the smallest? 4.4 ⋅ 10−5, 3.99 ⋅ 10−6, 2.6 ⋅ 102, 1.85 ⋅ 103

Step-by-step answer

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The answer is in the image

Mathematics

If a salesperson makes 6% commission, how much would they make from a $1,800 sale?

Step-by-step answer

P Answered by PhD

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

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the surface area of a box is 232 square inches. the box is 4 inches wide and 8 inches long. what is the hight?

Step-by-step answer

P Answered by PhD

The solution is given in the image below

Mathematics

If a european swallow flies 15 meters every 1 second how many would kilometers would it fly in 15 minutes

Step-by-step answer

P Answered by PhD

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

Mathematics

David is building wooden picture frames. Each frame requires 3/4 feet of wood. If David started with 12 feet of wood and now has 6 feet of wood remaining, how many pictures frames has he built?

Step-by-step answer

P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Mathematics

Mathematics, 26.03.2020 20:52, mohammadhosseinkarim David is building wooden picture frames. Each frame requires 3/4 feet of wood. If David started with 12 feet of wood and now has 6 feet of wood remaining, how many pictures frames has he built?

Step-by-step answer

P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

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Rich is comparing the cost of maintaining his car with the depreciation value of the car. The value starts at $20,000 and decreases by 15% each year. The maintanance cost is $500 the first year and increases by 28% per year. When will the maintenance cost and the value be the same.

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