Question

"The two points shown are ordered pairs for an exponential function y = f(x). Write the formula for f. Be sure to use proper function notation. y (2,24.5) (1, 14)"

Answer 1

The formula for the exponential function f(x) using the given points (2,24.5) and (1,14) is f(x) = 8 * 1.75^x.

Step-by-step explanation:

The given points are (2,24.5) and (1,14). We can use the formula y = ab^x, where a is the y-intercept and b is the base of the exponential function. We can rewrite the points as equations:

24.5 = ab^2

14 = ab^1

We can then solve these two equations to find the values of a and b. Dividing the second equation by the first equation, we get:

14/24.5 = b^1/b^2

Simplifying, we have:

14/24.5 = b^1-2

14/24.5 = b^-1

Multiplying both sides by 24.5, we get:

14 = 24.5/b

Dividing both sides by 24.5, we find that b is approximately 1.75. Substituting this value of b back into the first equation, we have:

24.5 = a(1.75)^2

Simplifying, we get:

24.5 = 3.0625a

Dividing both sides by 3.0625, we find that a is approximately 8.

Therefore, the formula for f(x) is f(x) = 8 * 1.75^x.