Question

which of the following is an equivalent function to the function below? f(x) = 50(1.05)12x f(x) = 50(1.7959)x f(x) = 50(12.6000)x f(x) = 600(1.05)x f(x) = 4.2(1.05)x

Answer 1

Hello,

Since 1.05^12=1,795856326022129150390625≠1.7959

50*1.05^(12x)=50*((1.05^^12)^x)=50*1.759^x

Answer A

Answer 2

The equivalent function is
`f(x)=50(1.7959)^(x)`

Explanation:

We have been given the function
`f(x)=50(1.05)^(12x)`

and we have to find an equivalent function. In order to find the same first of all we can use the below exponent property.

`x^(ab) = (x^(a))^b`

Using the above property the given function will become,

`f(x)=50(1.05)^(12x)=50((1.05)^(12))^x`

Now
`(1.05)^(12)=1.7959`

So, the equivalent function is
`f(x)=50(1.7959)^(x)`

Thus, Option (1) is correct.