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Ghella [55]
3 years ago
12

Ice skates on sale for 25% off cost $45. What is the regular price of the skates? a. $56.25 c. $70 b. $60 d. $80

Mathematics
2 answers:
vodomira [7]3 years ago
4 0
The answer is A. $56.25
Reika [66]3 years ago
4 0
45 / 0.75 = 60

answer is <span>b. $60</span>
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2 years ago
Jack bought a new car in 2014 for 28,000. If the value of the car decreases by 14% each year, write an exponential model for the
elena55 [62]

Answer:

In 2026 car will have a value of $5,000.

Step-by-step explanation:

We have been given that Jack bought a new car in 2014 for 28,000. If the value of the car decreases by 14% each year.

Since we know that an exponential function is in form: y=a*b^x, where,

a = Initial value,

b = For decay or decrease b is in form (1-r), where r represents decay rate in decimal form.

Let us convert our given decay rate in decimal form.

14\%=\frac{14}{100}=0.14

Upon substituting a =28,000 and r=0.14 in exponential decay function we will get,

y=28,000(1-0.14)^x, where x represents number of years after 2014.

Therefore, the function y=28,000(0.86)^x represents the value of car x years after 2014.

To find the number of years it will take to car have the value of $5,000, we will substitute y=5,000 in our function.

5,000=28,000(0.86)^x

Let us divide both sides of our equation by 28,000.

\frac{5,000}{28,000}=\frac{28,000(0.86)^x}{28,000}

0.1785714285714286=(0.86)^x

Let us take natural log of both sides of our equation.

ln(0.1785714285714286)=ln((0.86)^x)

Using natural log property ln(a^b)=b*ln(a) we will get,

ln(0.1785714285714286)=x*ln(0.86)

\frac{ln(0.1785714285714286)}{ln(0.86)}=\frac{x*ln(0.86)}{ln(0.86)}

\frac{-1.7227665977411033893}{-0.1508228897345836}=x

x=11.422447\approx 12  

As in the 12th year after 2014 car will have a value of $5,000, so we will add 12 to 2014 to find the year.

2014+12=2026

Therefore, in 2026 car will have a value of $5,000.

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