Question

Select the situation in which one quantity is changing at a constant rate in relation to the other quantity.

Answer 1

Answer:

A. Barry spends $9 on lunch daily.

Step-by-step explanation:

We are required,

To find the situation in which one constant is changing at a constant rate in relation to the other quantity.

So, according to the options, we have,

A. Barry spends $9 on lunch daily.

Let x= number of days and as the cost of lunch each day is $9

Then, the total cost of the lunch y, is $y=9x$

Thus, this situation changes the variable with constant rate.

B. The market value of a new computer decreases by 6% every year.

Let, a= fixed initial value of the computer and x= number of years.

Since, the rate of decrease in value = 6% = 0.06

Then, the market value of the computer per year, y, is given by,

$y=a(1-0.06)^x\\\\y=a(0.94)^x$

Thus, this situation changes the variable exponentially.

C. Nathan's investments increase in value by 13.5% each month.  

Let, a= fixed initial investment and x= number of months.

Since, the rate of increase = 13.5% = 0.135

Then, the investment per month, y, is given by,

$y=a(1+0.135)^x\\\\y=a(1.135)^x$

Thus, this situation changes the variable exponentially.

D. The number of ants in a colony doubles every 8 weeks.

Let, x= number of weeks where 'x' belongs to the se {1,8,16,24,...}.

Since, the number of ants is doubling every 8 weeks.

So, the number of ants in the colony, y, is $y=2^x$

Thus, this situation changes the variable exponentially.

Hence, the situation that changes the variables with a constant rate is A.

Answer 2

Choice A is the only one that is changing at a constant rate. The reason is that for all three other choices the new rate is based on a different amount after the percent has been applied or the doubling of the ants has been applied. The price per day for the lunch Is constant because whatever the number of days is the amount would always stay the same for each of those days.