Question

Write an exponential function in the form y=ab^x that goes through points (0, 7) and (5,1701).

Answer 1

Refer to the attached image

Answer 2

An exponential function has the form y = ab^x, where a is the initial value and b is the common ratio. To find the function that goes through the points (0, 7) and (5, 1701), we can use these points to find the values of a and b.

First, we can plug in the point (0, 7) into the exponential function and solve for a:

y = ab^x

7 = a(b^0)

7 = a

So, a = 7.

Next, we can use the point (5, 1701) to find the value of b. We know that:

y = ab^x

1701 = 7b^5

So, b = (1701/7)^(1/5)

Now that we have the values of a and b, we can write the exponential function that goes through the points (0, 7) and (5, 1701) as:

y = 7( (1701/7)^(1/5) )^x

y = 7( (1701/7)^(1/5) )^x

y = 7* (1701^(1/5))^x

y = 7* (1701^(1/5))^x

This is the exponential function that goes through the points (0, 7) and (5, 1701).

Explanation: