A tire can hold C cubic feet of air. It loses a percentage of its air during each period of time, t. This rate of loss, written as a decimal, is r. This situation can be described using the following formula: C(1-r)^1. What effect, if any, does increasing the value of r have on the value of C?
Well, increasing the value of r would result in a higher rate of air loss from the tire. So, in this case, the effect of increasing r would be a decrease in the value of C because more air is being lost. It's like the tire deciding to go on a spontaneous diet, getting lighter and losing some of its air along the way. Talk about commitment to weight loss! Just remember, if you start to see your tire looking a little deflated, maybe it's time to give it some air, or perhaps a hearty meal.
Increasing the value of r will have a decreasing effect on the value of C.
To understand the effect of increasing the value of r on the value of C, let's break down the formula provided: C(1 - r)^1.
In this formula, C represents the initial capacity or volume of air that the tire can hold (given in cubic feet). The term (1 - r)^1 represents the rate at which the tire loses air during each time period.
To interpret the formula, (1 - r) is derived by subtracting the rate of air loss (r) from 1, representing the percentage of air that remains after the loss. As we raise this to the power of 1, it does not have any impact on the expression.
Therefore, the formula simplifies to C(1 - r). We can interpret this as the remaining percentage of air in the tire after the loss is multiplied by the initial volume, giving us the final volume of air in the tire.
Now, back to your question - what effect does increasing the value of r have on the value of C?
Increasing the value of r will lead to a higher rate of air loss during each time period. As a result, the remaining percentage of air (1 - r) will be smaller, leading to a larger decrease in volume when multiplied by the initial capacity (C).
So, increasing the value of r will have a negative effect on the value of C. It will cause the tire to lose more air, reducing its overall capacity.
increasing r means that 1-r is less
what happens when you raise a smaller fraction to a power?
You are multiplying by a smaller number, so ...