What is the 15 the term

Write an exponential equation in the form y = abx whose graph passes through points (4, 8) and (6, 32).

Artist 52 [7]

Answer:

Option C.

Step-by-step explanation:

The general exponential equation is

$y=ab^x$

It is given that the graph of exponential function passes through points (4,8) and (6,32). It means the equation of exponential function must be satisfied by these points.

$8=ab^4$ ...(1)

$32=ab^6$ ...(2)

Divide equation (2) by equation (1).

$\dfrac{32}{8}=\dfrac{ab^6}{ab^4}$

$4=b^2$

Taking square root on both sides.

$2=b$

Put b=2 in (1).

$8=a(2)^4$

$8=16a$

$\dfrac{8}{16}=a$

$0.5=a$

Substitute a=0.5 and b=2 in the given general exponential equation.

$y=0.5(2)^x$

Therefore, the correct option is C.

8 0

3 years ago

Steve puts an 18-foot ladder against his house. The ladder reaches a height of 15 feet on the house. How far is the bottom of th

krek1111 [17]

Answer:

$3 \sqrt{11}$

Step-by-step explanation:

Since we are given the hypotenuse which is 18 since it slanted, and leans on the house. And we are given one of the legs which is 15 since it is vertical. We can use the pythagorean theorem to solve for this problem.

${a}^{2} + {b}^{2} = c {}^{2}$

where a and b are the legs and c is the hypotenuse l.

Let plug it in

${a}^{2} + 15 {}^{2} = {18}^{2}$

${a }^{2} + 225 = 324$

${a}^{2} = 99$

$a = \sqrt{99}$

$a = \sqrt{9 \times 11}$

$a = 3 \sqrt{11}$

4 0

3 years ago

The graph shown represents the number of bacteria in a dish after a certain number of minutes. It is a function in the form f(x)

SSSSS [86.1K]

Answer:

The number of bacteria in the dish after 9.9 minutes is 478

Step-by-step explanation:

The form of the function is $f(x)=a.b^{x}$ , where a is the initial amount (value f(x) at x = 0)

To find a and b let us use two points from the graph and substitute their coordinates in the equation

∵ The graph passes through point (1 , 1)

∴ x = 1 and y = 1

- Substitute them in the equation

∵ $1=a.b^{1}$

∴ a.b = 1 ⇒ (1)

∵ The graph passes through point (1 , 1)

∴ x = 3 and y = 4

- Substitute them in the equation

∵ $4=a.b^{3}$

∴ a.b³ = 4 ⇒ (2)

Use equation (1) to find a in terms of b

∵ a.b = 1

- Divide both sides by b

∴ $a=\frac{1}{b}$ ⇒ (3)

- Substitute a in equation (2) by equation (3)

∴ $\frac{1}{b}$ . b³ = 4

- Remember the rule $\frac{a^{m}}{a^{n}}=a^{m-n}$

∵ $\frac{1}{b}$ . b³ = $b^{3-1}$ = b²

∴ b² = 4

- Take √ for both sides

∴ b = 2

Substitute the value of b in equation (3) to find a

∵ a = $\frac{1}{2}$

∴ a = 0.5

∴ $f(x)=0.5(2)^{x}$

∵ f(x) represents the number of bacteria after x minutes

∵ x = 9.9 minutes

- Substitute x by 9.9 to find the number of bacteria

∵ $f(9.9)=0.5(2)^{9.9}$

∴ f(9.9) = 477.7128917

- Round it to the nearest whole number

∴ f(9.9) = 478

∴ The number of bacteria in the dish after 9.9 minutes is 478

4 0

3 years ago

A rectangular sign must have an arae of 43 square yards. its lenght must be 2 yards more than its width. find the dimensions of

inna [77]

We know A=L•W so set 43 equal to A. Equation should look like this thus far: 43=L•W. Now when the question says more than we know that means adding. Since we don’t know the width let w=width. So know your equation should look like this: 43=2+w•(w). Knowing this equation you should be able to solve for the dimensions of the sign. If you need help on that let me know.

8 0

3 years ago

Find the surface area of the prism.

Elanso [62]

Answer: 26

Step-by-step explanation:

I would say 26 because you multiplying 3 and 4 and then add whatever number you get for 8 and 5.

3 0

2 years ago

What is the 15 the term​

What is the 15 the term