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write-an-equation-for-an-exponential-function.md

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1. You are given the table of values below for an exponential function. Write an equation that models it.
x y
0 1
1 4
2 16
3 64
Click the arrow for the answer.

Answer: The equation is y = 4x.

The general form of an exponential function is y = abx. So, you need to solve for a and b, and then substitute them into the equation.

Here, at x = 0, y = 1, so a = 1. To get b, notice that each y-value is multiplied by a factor of 4.

An alternative way to get b is as follows. Using a = 1 from above, and given that the function is exponential, choose a point. Let's choose (1,4). Plug the point (1,4) into the general form of an exponential equation.

Solving, you get b = 4.

2. You are given the table of values below for an exponential function. Write an equation that models it.
x y
0 8
1 2
2 0.5
Click the arrow for the answer.

Answer: The equation is:

The general form of an exponential function is y = abx. So, you need to solve for a and b, and then substitute them into the equation.

Here, at x = 0, y = 8, so a = 8. To get b, notice that each y-value is multiplied by 0.25 = 1/4.

Alternative Explanation:

An alternative way to get b is as follows. Using a = 8 from above, and given that the function is exponential, choose a point. Let's choose (1,2). Plug the point (1,2) into the general form of an exponential equation.

Solving, you get b = 1/4.

3. You are given the table of values below for an exponential function. Write an equation that models it.
x y
0 4
1 12
2 36
3 108
Click the arrow for the answer.

Answer: The equation is:

The general form of an exponential function is y = abx. So, you need to solve for a and b, and then substitute them into the equation.

Here, at x = 0, y = 4. no matter the value of b, so a = 4. You can then plug in x = 1 and y = 12 to find that