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3 years ago

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Based on the pattern, what are the next two terms of the sequence? 9, 95, 925, 9125 , 9625, ... 9630, 93130 93125,915625 9630.96

35 93125, 93130

1 answer:

likoan [24]3 years ago

8 0

It appears that the digit 9 is prepended to each term of the sequence 5^(n-1).

The next two terms will be 5^5 and 5^6, each with 9 prepended: 93125 and 915625.

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You purchase a stereo system for $830. The value of the stereo system decreases 13% each year. a. Write an exponential decay mod

lorasvet [3.4K]

Answer:

a. $y=830*(0.87)^x$

b. The value of stereo system after 2 years will be $628.23.

c. After approximately 4.98 years the stereo will be worth half the original value.

Step-by-step explanation:

Let x be the number of years.

We have been given that you purchased a stereo system for $830. The value of the stereo system decreases 13% each year.

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

a = Initial value,

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

Let us convert our given rate in decimal form.

$13\%=\frac{13}{100}=0.13$

Upon substituting our given values in exponential decay function we will get

$y=830*(1-0.13)^x$

$y=830*(0.87)^x$

Therefore, the exponential model $y=830*(0.87)^x$ represents the value of the stereo system in terms of the number of years since the purchase.

b. To find the value of stereo system after 2 years we will substitute x=2 in our model.

$y=830*(0.87)^2$

$y=830*0.7569$

$y=628.227\approx 628.23$

Therefore, the value of stereo system after 2 years will be $628.23.

c. The half of the original price will be $\frac{830}{2}=415$ .

Let us substitute y=415 in our model to find the time it will take the stereo to be worth half the original value.

$415=830*(0.87)^x$

Upon dividing both sides of our equation by 830 we will get,

$\frac{415}{830}=\frac{830*(0.87)^x}{830}$

$0.5=0.87^x$

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

$ln(0.5)=ln(0.87^x)$

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

$ln(0.5)=x*ln(0.87)$

$\frac{ln(0.5)}{ln(0.87)}=\frac{x*ln(0.87)}{ln(0.87)}$

$\frac{ln(0.5)}{ln(0.87)}=x$

$\frac{-0.6931471805599}{-0.139262067}=x$

$x=4.977286\approx 4.98$

Therefore, after approximately 4.98 years the stereo will be worth half the original value.

5 0

3 years ago

Witch value from the set {3,8,9,14} makes the euation true 2n-5=

lutik1710 [3]

The value from the set {3,8,9,14} makes the equation 2n - 5 = 11 true is n = 8

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

2n - 5 = 11

When n = 3:

2(3) - 5 = 1 ≠ 11

When n = 8:

2(8) - 5 = 11

When n = 9:

2(9) - 5 = 13

When n = 14:

2(14) - 5 = 23

The value from the set {3,8,9,14} makes the equation 2n - 5 = 11 true is n = 8

Find out more on equation at: brainly.com/question/2972832

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3 0

2 years ago

Sketch a cylinder with radius 8 feet and height 3 feet, then find the volume.

4vir4ik [10]

Answer: 339.29ft^3

Step-by-step explanation:

The formula for a cylinder is πr^2h

In your scenario, r=8 and h=3 so put those into the equation -

π8^2(3) and just solve!

7 0

3 years ago

Figure ABCD is a parallelogram. What is the value of n?

Zigmanuir [339]

Answer

Find out the what is the value of n.

To prove

By using the parallelogram property .

In parallelogram opposite angels are congruent .

As shown in the figure .

∠B = ∠ D

As given

∠B = (2n + 32)°

∠D = (4n - 2)°

(2n + 32) = (4n - 2)

solving the above

4n -2n = 32 +2

2n = 34

$n = \frac{34}{2}$

n = 17

Therefore the value of n is 17 .

5 0

3 years ago

Read 2 more answers

Solve the inequality x+1<3/4 and write the solution in interval notation.

Darya [45]

The solution to the inequality in interval form is (-∞, -1/4)

<h3>Inequality expressions</h3>

Inequality are expressions not separates by an equal sign. Given the inequality below;

x+1<3/4

Subtract 1 from both sides to have;

x + 1 - 1 < 3/4 - 1

x < 3/4 - 1

x < (3-4)/4

x < -1/4

Hence the solution to the inequality in interval form is (-∞, -1/4)

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3 0

1 year ago