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3 years ago

The first tern of an arithmetic sequence is -3 and the fifteenth term id 53. What is the common difference of the sequence?

1 answer:

5 0

The common difference is 4. U know that the formula is the first term + d(n -1). N-1 is 14 so u know that 14 times a number needs to equal 56 because the first term is -3 and 56-3 is 53. 14 * 4 is 56. So the common difference is 4

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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.

6 0

3 years ago

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How do you work out 15% of 80000

S_A_V [24]

Multiply 0.15 and 80,000. Your answer is 12,000

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15. How can we exhibit the 9 fruit of the spirit more in our lives to be better people, and eventually

olga nikolaevna [1]

We are submissive to God's commands and desire the good of others when our actions are motivated by genuine kindness of heart and exhibit the fruit of the Spirit.

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2 years ago

walter buys a bus pass for 30$. everytime he rides the bus money is deducted from the value pass. he rode 12 times and 24$ was d

astra-53 [7]

To solve this, set up a proportion and solve.

$\frac{12}{24}= \frac{1}{x} \\ \\ 12*x=24*1 \\ \\ 12x=24 \\ \\ x=2$

It cost $2 per ride.

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3 years ago

Chris has 5 1/2cups of water in a pitcher. He pours 3/8 cup of water into a glass. How many cups of water is left in the pitcher

igomit [66]

Answer: The Answer is 5 1/8.

Step-by-step explanation:

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