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Rom4ik [11]
2 years ago
15

Jace purchases a new motorcycle for $8000. The bike depreciates 12% every year.

Mathematics
1 answer:
Alex777 [14]2 years ago
3 0

Answer:

We know that the original price of the bike was $8,000.

After one year, the price of the bike decays a 12%, then the new price of the bike is:

P(1) = $8,000*( 1 - 12%/100%) = $8,000*(1 - 0.12)

After another year, the price again decays a 12%, the new price will be:

P(2) = $8,000*(1 - 0.12)*(1 - 12%/100%) = $8,000*(1 - 0.12)*(1 - 0.12) = $8,000*(1 - 0.12)^2

We already can see the pattern here, after t years, the price of the bike will be:

P(t) = $8,000*(1 - 0.12)^t

With this equation, we can find the price of the bike after 5 years, where we only need to replace t by 5

We will get:

P(5) = $8,000*(1 - 0.12)^5 = $4,221.9

The price of the bike after 5 years is  $4,221.9.

Now we want two equations to represent this, so we need another.

This is kinda trivial, because there is only one equation that represents this, so we only can rewrite our equation in another form.

We could say that the price of the bike after t years is:

P(t) = $8,000*(0.88)^t

or something like:

P(t) = $7040*(0.88)^(t - 1)

Where i multiplied the initial value by 0.88, and then reduced the exponent by one.

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Answer:

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Step-by-step explanation:

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2 years ago
Helen is putting a fence around her flower garden, which is in the shape of half of a circle and a rectangle. If the semicircle
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Answer:

Part 1) Helen will need 38 feet of fencing

Part 2) The perimeter around the three sides of the rectangular section of the garden is 27 feet

Part 3) The approximate distance around half of the circle is 11 feet

Step-by-step explanation:

Part 1) How much fencing will Helen need?

Find out the perimeter

we know that

The perimeter of the figure is equal to the sum of three sides of the rectangular section plus the circumference of a semicircle

so

P=2L+W+\frac{1}{2}\pi D

we have

L=10\ ft\\W=7\ ft\\D=7\ ft\\\pi =\frac{22}{7}

substitute

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therefore

Helen will need 38 feet of fencing

Part 2)  What is the perimeter around the three sides of the rectangular section of the garden?

P=2L+W

we have

L=10\ ft\\W=7\ ft

substitute

P=2(10)+7

P=20+7=27\ ft

therefore

The perimeter around the three sides of the rectangular section of the garden is 27 feet

Part 3) What is the approximate distance around half of the circle?

Find the circumference of semicircle

C=\frac{1}{2}\pi D

we have

D=7\ ft\\\pi =\frac{22}{7}

substitute

C=\frac{1}{2}(\frac{22}{7})(7)

C=11\ ft

therefore

The approximate distance around half of the circle is 11 feet

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