Answer:
y = 3 * 9^x
Explanation:
To write an exponential function in the form y = ab that goes through the points (0, 3) and (2, 243), we need to find the values of a and b.
Let's start by using the point (0, 3). When x = 0, y = 3. Substituting these values into the exponential function equation, we get:
3 = ab^0
3 = a * 1
a = 3
Now, let's use the second point (2, 243). When x = 2, y = 243. Substituting these values into the exponential function equation, we get:
243 = 3b^2
To find the value of b, we can rewrite the equation as:
3b^2 = 243
Dividing both sides of the equation by 3, we have:
b^2 = 81
Taking the square root of both sides, we get:
b = ±9
Since we are looking for a positive value for b, we can take b = 9.
Therefore, the exponential function that goes through the points (0, 3) and (2, 243) is: y = 3 * 9^x