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larisa [96]
2 years ago
13

The table below shows the value of a car during certain years . Using an exponential model , write an equation for the curve of

best fit, then estimate the value of the car in 2016 .​

Mathematics
2 answers:
blondinia [14]2 years ago
8 0

The exponential function that gives the value of the car in t years after 2008 is:

A(t) = 27500(0.88)^t.

Using the function, the estimate for the value of the car in 2016 is of $9,900.

<h3>What is an exponential function?</h3>

A decaying exponential function is modeled by:

A(t) = A(0)(1 - r)^t

In which:

  • A(0) is the initial value.
  • r is the decay rate, as a decimal.

In this problem:

  • The initial value is of A(0) = 27,500.
  • Considering the first year change, we have that 1 - r = 24200/27500 = 0.88.

Hence, the equation is:

A(t) = 27500(0.88)^t

2016 is 8 years after 2008, hence the value of the car will be given by:

A(8) = 27500(0.88)^8 = 9900

More can be learned about exponential functions at brainly.com/question/25537936

vova2212 [387]2 years ago
6 0

The exponential function is given as y = 27500(0.88)ˣ and the value of the car in 2016 is $9890

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

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

Let y represent the value of the car after x years after 2008, hence:

at x = 0, y = 27500

27500 = ab⁰

a = 27500

At x = 1, y = 24200, hence:

24200 = 27500b¹

b = 0.88

y = 27500(0.88)ˣ

In 2016, x = 8, hence:

y = 27500(0.88)⁸ = 9890

The exponential function is given as y = 27500(0.88)ˣ and the value of the car in 2016 is $9890

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

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Answer: 121.126

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7 0
4 years ago
How much money should be deposited today in an account that earns 7% compounded semiannually so that it will accumulate to $12,0
Korvikt [17]

Given rate is = 7% or 0.07

Total amount needed = $12000

Time = 4 years

Here, the  deposit is  compounded semiannually, means twice per year and this gives 8 annual compounding periods in 4 years.

The equation becomes:

P= \frac{12000}{(1+\frac{0.07}{2})^{2.4}}

P = \frac{12000}{1.035^{8}}

Solving it, we get P = $ 9112.93

Hence $9112.93 should be deposited today.



3 0
3 years ago
Please help with this
Arturiano [62]

Answer:

10x^2 -4x +6

Step-by-step explanation:

The area of the blue square is

2* 5x^2 = 10x^2

The area of the pink square is

2 * -2x = -4x

The area of the green square is

2 *3 = 6

Add it all together

10x^2 -4x +6

4 0
3 years ago
enkeli has a bottle that holds 2.4 liters of juice. he divides it evenly into 6 cups. how many milliliters of juice does each of
liberstina [14]

Answer:400

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3 0
3 years ago
I DONT KNOW THESE! HELP!
kkurt [141]

Answer:

20. x = 5, y = -2

21. x = 11, y = 12

22. x = 22, y = 11

23. x = 11, y = 10

Step-by-step explanation:

20. Opposite sides in the parallelogram are congruent, so

2y+18=3x-1\\ \\6x-3=17-5y

Solve this system of two equations:

\left\{\begin{array}{l}2y-3x=-19\\ \\6x+5y=20\end{array}\right.

Multiply the first equation by 2 and add two equations:

2(2y-3x)+6x+5y=2\cdot (-19)+20\\ \\4y-6x+6x+5y=-38+20\\ \\9y=-18\\ \\y=-2

Substitute it into the first equation:

2\cdot (-2)-3x=-19\\ \\-3x=-19+4\\ \\-3x=-15\\ \\x=5

21. Opposite angles in the parallelogram are congruent, so

11x+5=10y+6

Consecutive angles are supplementary, so

6x-y+11x+5=180^{\circ}

Solve this system of two equations:

\left\{\begin{array}{l}11x-10y=1\\ \\17x-y=175\end{array}\right.

From the second equation

y=17x-175

Substitute it into the first equation:

11x-10(17x-175)=1\\ \\11x-170x+1750=1\\ \\-159x=-1749\\ \\x=11\\ \\y=17\cdot 11-175=187-175=12

22. Opposite angles in the parallelogram are congruent, so

2x-5=3y-12

Consecutive angles are supplementary, so

2x-5+7y+x=180^{\circ}

Solve this system of two equations:

\left\{\begin{array}{l}2x-3y=-7\\ \\3x+7y=185\end{array}\right.

From the first equation

x=-3.5+1.5y

Substitute it into the second equation:

3(-3.5+1.5y)+7y=185\\ \\-10.5+4.5y+7y=185\\ \\-105+45y+70y=1,850\\ \\115y=1,850+105\\ \\115y=1,955\\ \\y=17\\ \\x=-3.5+1.5\cdot 17=22

23. Opposite sides in the parallelogram are congruent, so

2x+9=4y-9\\ \\3x-5=2y+8

Solve this system of two equations:

\left\{\begin{array}{l}2x-4y=-18\\ \\3x-2y=13\end{array}\right.

Multiply the second equation by 2 and subtract it from the first equation:

2x-4y-2(3x-2y)=-18-2\cdot 13\\ \\2x-4y-6x+4y=-18-26\\ \\-4x=-44\\ \\x=11

Substitute it into the first equation:

2\cdot 11-4y=-18\\ \\-4y=-18-22\\ \\-4y=-40\\ \\y=10

3 0
3 years ago
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