Answer: y = 4.2 * (4.298)^x.
Explanation:
The given equation is y = ab^x, and we are given two points on the graph of this equation: (0, 4.2) and (2, 77.5).
To find the values of a, b, and the equation itself, we can use the given points. Let's start by plugging in the coordinates of the first point, (0, 4.2):
4.2 = ab^0
Any number raised to the power of 0 is equal to 1. So, we can simplify the equation to:
4.2 = a(1)
This means that a = 4.2.
Now let's move on to the second point, (2, 77.5). We'll plug in these values into the equation:
77.5 = ab^2
Since we know the value of a (which is 4.2), we can substitute it into the equation:
77.5 = 4.2b^2
To solve for b, we need to isolate it on one side of the equation. Let's divide both sides by 4.2:
77.5/4.2 = b^2
18.45 = b^2
To find the value of b, we can take the square root of both sides of the equation:
b = √18.45
b ≈ 4.298
Now that we have the values of a and b, we can write the equation y = ab^x:
y = 4.2 * (4.298)^x
Therefore, the equation that represents the given points (0, 4.2) and (2, 77.5) is y = 4.2 * (4.298)^x.
Hope this helps.