Question

Write an exponential function in the form y = a * b ^ x that goes through points (0, 14) and (4, 8750)

Answer 1

y=14(5)^x

Explanation:

Answer 2

Given:

An exponential function goes through points (0, 14) and (4, 8750).

To find:

The function.

Solution:

The general form of an exponential function is

`y=ab^x` ...(i)

It goes through points (0, 14) and (4, 8750). It means the the equation must be satisfied by these points.

Putting x=0 and y=14 in (i), we get

`14=ab^0`

`14=a`

The value of a is 14.

Putting a=14, x=4 and y=8750 in (i), we get

`8750=14b^(4)`

`(8750)/(14)=b^(4)`

`625=b^(4)`

It can be written as

`5^4=b^(4)`

`5=b`

The value of b is 5.

Putting a=14 and b=5 in (i), we get

`y=14b^5`

Therefore, the required exponential function is
`y=14b^5`.