Describe the transformation f(x)=-2x-4;r(x)=(1/2x)

If f(x) is an exponential function where f(-1.5) 26 and

mariarad [96]

Answer:

$f(10) = 1147.25$

Step-by-step explanation:

Given

$f(-1.5) = 26$

$f(5.5) = 7$

Required

f(10)

An exponential function is represented as:

$f(x) = ab^x$

$f(-1.5) = 26$ impleies that:

$26 = ab^{-1.5}$ --- (1)

$f(5.5) = 7$ implies that

$7 = ab^{5.5}$ --- (2)

Divide (2) by (1)

$26/7 = ab^{-1.5}/ab^{5.5}$

$3.71429 = b^{-1.5+5.5}$

$3.71429 = b^{4}$

Take 4th root

$b = 1.39$

Substitute $b = 1.39$ in $26 = ab^{-1.5}$

$26 = a * 1.39^{-1.5}$

$26 = a * 0.6102$

Solve for (a)

$a = 26/0.6102$

$a = 42.61$

f(10) is calculated as:

$f(10) = ab^{10}$

$f(10) = 42.61 * 1.39^{10}$

$f(10) = 1147.25$

3 0

3 years ago

After 2 years, a certain car is worth $16600. When it is 9 years old, the same car is then worth

Lubov Fominskaja [6]

The linear function that describes the situation is:

y = -950x + 18500.

The slope of -950 means that the price of the car decays $950 per year.

The y-intercept of 18500 means that the initial value of the car is of $18,500.

The x-intercept of 19.47 means that the value of car is of $0 after 19.47 years.

<h3>What is a linear function?</h3>

A linear function is modeled by:

$y = mx + b$

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0.

In this problem, in 7 years, the price of the car decays by $6,650, hence the slope is given by:

m = -6650/7 = -950.

The slope of -950 means that the price of the car decays $950 per year.

Then, the equation is:

y = -950x + b.

After 2 years, a certain car is worth $16600, hence when x = 2, y = 16600, and:

16600 = -950(2) + b

b = 18500.

The equation is:

y = -950x + 18500.

The y-intercept of 18500 means that the initial value of the car is of $18,500.

The x-intercept is found when y = 0, hence:

-950x + 18500 = 0.

x = 18500/950

x = 19.47.

The x-intercept of 19.47 means that the value of car is of $0 after 19.47 years.

More can be learned about linear functions at brainly.com/question/24808124

8 0

2 years ago

Assume that it costs Apple approximately E(x) 25,600 + 100x + 0.012 dollars to manufacture x 32GB iPods in a day. (a) The averag

uranmaximum [27]

Answer:

(a) $C'(x)=\dfrac{x^2-2560000}{x^2}$

(b)x=1600, Minimum Average Cost Per iPod=$132

(c) $C''(x)=\dfrac{5120000}{x^3}$

The result, C''(1600) is positive, which means that the average cost is Concave up at the critical point, and the critical point is a minimum.

Step-by-step explanation:

Given that it costs Apple approximately $ C(x) to manufacture x 32GB iPods in a day, where:

$C(x)=25,600+100x+0.01x^2$

(a)The average cost per iPod when they manufacture x iPods in a day is given by:

$Cost \:Per \:iPod=\dfrac{C(x)}{x} =\dfrac{25,600+100x+0.01x^2}{x}$

The average cost per iPod is therefore:

$C'(x)=\dfrac{x^2-2560000}{x^2}$

(b)To minimize average cost of x iPods per day, we set the average cost per iPod=0 and solve for x.

$C'(x)=\dfrac{x^2-2560000}{x^2}=0\\x^2-2560000=0\\x^2=2560000\\x=\sqrt{2560000}=1600$

The resulting minimum average cost (at x=1600) is given as:

$Cost \:Per \:iPod=\dfrac{C(x)}{x} =\dfrac{25,600+100x+0.01x^2}{x}\\\dfrac{25,600+100(1600)+0.01(1600)^2}{1600}\\=\$132$

Second derivative test

(c)The answer above is a critical point for the average cost function. To show it is a minimum, we calculate the second derivative of the average cost function.

$C''(x)=\dfrac{5120000}{x^3}$

At the critical point, x=1600

$C''(1600)=\dfrac{5120000}{1600^3}=0.00125$

The result, C''(1600) is positive, which means that the average cost is Concave up at the critical point, and the critical point is a minimum.

3 0

3 years ago

Solve please: 1/5 (25-5a) = 4-a

Liono4ka [1.6K]

Answer: There is no solution.

Step-by-step explanation:

1.) 1 / 5 (25) + 1 / 5 (-5a) = 4 - a

2.) 5 - a = 4 - a

3.) 5 - a + a = 4 - a + a

4.) 5 = 4

The variable a is completely removed, leaving the final answer as 5 = 4, which isn't true.

8 0

3 years ago

Read 2 more answers

5.31x + 6.65 = 9.28 Explain please:)

Lisa [10]

Answer:

5.31x=9.28-6.65

5.31x=2.63

×=2.63/5.31

x=2.63

5.31

5 0

3 years ago