Question

Does the expression 1.016x represent a percent increase greater than 12% if the original amount is x? How could I rewrite the expression as a sum of two terms to explain why or why not?

Answer 1

The expression
`1.016x` does not represent a percent increase greater than 12%.

Explanation:

We are asked to find whether the expression
`1.016x` represent a percent increase greater than 12% if the original amount is x.

First of all, we will find 12% increase. The total amount after x% increase would be original amount plus 12% of original amount.

`\text{12 percent increase}=x+(12)/(100)x`

`\text{12 percent increase}=x+0.12x`

`\text{12 percent increase}=1.12x`

Since 1.12 is greater than 1.016, therefore, the expression
`1.016x` does not represent a percent increase greater than 12%.

We can rewrite
`1.016x` as:

`1.016x=1x+0.016x=x+0.016x`

Let us convert
`0.016` to percent by multiplying by 100.

`0.016* 100\%=1.6\%`

Since 1.6% is less than 12%, therefore, the expression
`1.016x` does not represent a percent increase greater than 12%.