Question

Find the exponential function of the form f(x)=c*aˣ that contains the two points shown below: (0,8) and (3,64)

Answer 1

To find the exponential function that contains two given points, substitute the x and y values into the equation and solve for the constants c and a.

Step-by-step explanation:

We can find the exponential function of the form f(x) = c * a^x that contains the two points (0,8) and (3,64) by substituting the x and y values into the equation and solving for c and a.

Let's start with the first point (0,8). Substitute x=0 and y=8 into the equation:

8 = c * a^0 = c * 1 = c

So we know that c = 8. Now let's substitute the second point (3,64) into the equation:

64 = 8 * a^3

Divide both sides by 8:

8 = a^3

Taking the cube root of both sides:

a = 2

Therefore, the exponential function that contains the two given points is f(x) = 8 * 2^x.

Answer 2

The exponential function that contains the points (0,8) and (3,64) is f(x) = 8*2x. We find this by solving for the constants c and a using the given points.

Step-by-step explanation:

To find the exponential function f(x)=c*ax that passes through the points (0,8) and (3,64), we can use these points to determine the constants c and a.

Using the first point (0,8), when we plug x = 0 into the function f(x)=c*ax, we get f(0)=c*a0=c, as any number to the zero power is 1. Therefore, c = 8.

Now, let's use the second point (3,64). Substituting x = 3 and the previously found c into the equation, we get 64 = 8*a3. Solving for 'a', we divide both sides by 8 yielding a3 = 64/8 = 8. Taking the cubic root of both sides gives us a=2. Therefore, our exponential function is f(x) = 8*2x.