Question

®

A candle 6 inches high burns at a rate of 1 inch every 2 hours for
5 hours. (Use interval notation for the domain and range of the
function that models this situation.)
The candles burning rate is
in./h.
The candles height h (in inches) at any time
t (in hours) is modeled by h(t) =
Since the candle burns for 5 hours, the domain is restricted to the
intervalo,
The range is

Answer 1

• 1/2 in/hour
• h(t) = 6 - 1/2t
• The Domain is: 0 ≤ t ≤ 5
• Range is: 3.5 ≤ h(t) ≤ 6

Explanation:

We have a candle that is 6 inches high, and burns at a rate of 1 inch every 2 hours.

First question:

We want to know what is the burning rate in in/hr:

With the information we have we know that the candle will burn 1 inch in 2 hours, so we have to divide by 2 to get how many inches will it burn in 1 hour:

1 inch/2

2 hours / 2

so we get that the burning rate is:

1/2 in/hr or 0.5 in/hr

The second questions say what is the height of the candle at any time by a function modeled by h(t), where h is the height (in inches) and t is the time (in hours).

We have to use the burning rate we just got and get the function:

h(t) = 6 - 1/2t We know that the height will be 6 inches minus 1/2 of the time in hours.

The third question is asking us for the domain of the function we just got (h(t) = 6 - 1/2t) if the candle burns for 5 hours:

The domain is all the values by which a function is defined, or in other words the values that "t" can get.

In this case, t can only be 0 or positive numbers because we can't have negative time so: t ≥ 0. And we know that it will only burn for 5 hours so t can't be greater than 5 so: t ≤ 5 or:

0 ≤ t ≤ 5

The last question is asking for the range, and the range of a function is all the numbers the dependent value can get after using all the domain values. In this case we will substitute the function by the lowest and greatest values t can get:

Lowest value of t = 0

h(0) = 6 - 1/2*0

h(0) = 6

Greatest value of t = 5

h(5) = 6 - 1/2*5

h(5) = 6 - 2.5

h(5) = 3.5

So h(t) can only have values between 3.5 and 6, so the range is:

3.5 ≤ h(t) ≤ 6

Answer 2

See explanation

Explanation:

A candle 6 inches high burns at a rate of 1 inch every 2 hours for 5 hours. The candles burning rate is 0.5 inch per hour).

Then

• a cnadle height after first hour is 6 - 0.5 = 5.5 inches;
• a candle height after first two hours is 5.5 - 0.5 = 5 inches;
• a candle height after first three hours is 5 - 0.5 = 4.5 inches;
• a candle height after first 4 hours is 4.5 - 0.5 = 4 inches;
• a candle height after first 5 hours is 4 - 0.5 = 3.5 inches.

The candles height h (in inches) at any time t (in hours) is modeled by

`h(t)=6-0.5t`

The domain of this function is

`0\le t\le 5`

The range og this function is

`3.5\le h(t)\le 6`