Question

What is the specific exponential function that passes through the points (2, 36) and (5, 972)?

a) y = 4x + 3
b) y = 4.38
c) y = 3.4%
d) y = 3x + 4

Answer 1

The specific exponential function that passes through the points (2, 36) and (5, 972) is y = 12(3^x).

Step-by-step explanation:

The specific exponential function that passes through the points (2, 36) and (5, 972) can be determined using the general form of an exponential function: y = ab^x. To find the values of a and b, we can use the given points.

Using the point (2, 36), we have 36 = ab^2. Using the point (5, 972), we have 972 = ab^5. Now we can solve these two equations simultaneously to find the values of a and b.

By substituting the value of a in the second equation from the first equation, we get b^3 = 27. Taking the cube root on both sides, we find that b = 3. Substituting this value into the first equation, we have 36 = 3a. Solving for a, we get a = 12. Therefore, the specific exponential function that passes through the given points is y = 12(3^x).