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: