Final answer:
The exponential function in the form y = abˣ that passes through the points (0, 7) and (2, 700) is y = 7 * 10ˣ.
Step-by-step explanation:
To write an exponential function in the form y = abˣ that passes through the points (0, 7) and (2, 700), we need to find the values of a and b. Let's first substitute the coordinates of the first point, (0, 7), into the equation:
7 = a * b⁰
Since any number raised to the power of 0 is 1, we have:
7 = a * 1
Therefore, a = 7.
Now, let's substitute the coordinates of the second point, (2, 700), into the equation:
700 = 7 * b²
Dividing both sides by 7, we get:
100 = b²
Taking the square root of both sides, we find:
b = 10
So, the exponential function in the form y = abˣ that passes through the points (0, 7) and (2, 700) is:
y = 7 * 10ˣ