Evaluate the expression. 8

An airplane 30,000 feet above the ground begins descending at a rate of 2,000 feet per minute. Write an equation to model the si

antiseptic1488 [7]

A = 30,000 - 2000m where A=altitude and m = number of minutes

After 5 minutes A ( altitude) = 30,000 - 2000(5) = 20,000 feet

6 0

3 years ago

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

Factor the expression completely. 9x+6

Kamila [148]

Answer:

3(3x+2)

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

HURRY!!

scoundrel [369]

Answer:

I'm sorry you got that wrong. The correct answer was R since it is staying in the same place which is called a constant line. It stays in the same place since she isn't moving, she is just standing there waiting for the cab.

4 0

3 years ago

The ten's digit of a two digit number is 1 more than 4 times the units' digit. if 63 is subtracted from the number, the order of

ser-zykov [4K]

Let x be the digit in the tens place and y be the digit in the ones place.
so, the digit is xy

The ten's digit of a two digit number is 1 more than 4 times the units' digit.
x = 4y + 1

63 is subtracted from the number, the order of the digits is reversed
10x + y - 63 = 10y + x
9x - 9y = 63

x = 4y + 1 ------------ (1)
9x - 9y = 63 ---------- (2)

Sub (1) into (2)
9(4y + 1) - 9y = 63
36y + 9 - 9y = 63
27y = 63 - 9
27y = 54
y = 2 ------- sub into (1)

x = 4(2) + 1 = 9

x = 9, y = 2
The number is 92

3 0

3 years ago

Evaluate the expression. 8 - 9: (7 + 2)