Question

Find an exponential function of the form f(x) = ba^x that has the given y-intercept and passes through the point P.

y-intercept 9;
P(2, 1)
f(x) = ?

Answer 1

The exponential function with a y-intercept of 9 and passing through the point P(2, 1) is f(x) = 9 * (1/3)^x.

Step-by-step explanation:

To find an exponential function of the form f(x) = ba^x that has a given y-intercept of 9 and passes through the point P(2, 1), we need to set up two equations based on the given information. When x=0, the function must equal 9 (the y-intercept), so we have:

1) f(0) = b * a^0 = b, which simplifies to b = 9.

Then, since the function must pass through point P(2, 1), we use this point to create a second equation:

2) f(2) = 9 * a^2 = 1.

Solving this equation for a, we get a^2 = \(\frac{1}{9}\), which means a = \(\frac{1}{3}\).

So, the exponential function is:

f(x) = 9 * (\(\frac{1}{3}\))^x.