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

Answer:

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

Step-by-step 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.

$\text{12 percent increase}=x+\frac{12}{100}x$

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

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

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.

$0.016\times 100\%=1.6\%$

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