Question

Write an exponential function in the form y equals a left parenthesis b right parenthesis to the power of x that contains the points open parentheses 1 comma space 15 close parentheses and open parentheses 3 comma space 375 close parentheses. Use the f subscript x key to type it in this form.

Answer 1

Answer:To write an exponential function in the form y = a(b)^x that passes through the points (1, 15) and (3, 375), we need to find the values of a and b.

1) Let's start by substituting the coordinates of the first point, (1, 15), into the equation. This gives us the equation:

15 = a(b)^1

Since any number raised to the power of 1 is itself, the equation simplifies to:

15 = ab

2) Next, let's substitute the coordinates of the second point, (3, 375), into the equation. This gives us the equation:

375 = a(b)^3

3) Now, we can divide the equation we obtained in step 2 by the equation we obtained in step 1:

375 / 15 = a(b)^3 / ab

Simplifying further:

25 = b^2

4) Taking the square root of both sides of the equation, we find:

b = ±5

5) Now, let's substitute the value of b back into the equation we obtained in step 1:

15 = ab

If b = 5, then we have:

15 = 5a

Simplifying further:

a = 3

If b = -5, then we have:

15 = -5a

Simplifying further:

a = -3

Therefore, the exponential function that satisfies the given conditions is:

y = 3(5)^x or y = -3(-5)^x

Either of these equations can represent an exponential function that passes through the points (1, 15) and (3, 375).

Explanation: