y varies directly with x, and y=2. What is the value of y when x=5?
undetectable) in 20 hours. There
exists a set of ordered pairs (t, m),
where t is the amount of time in hours
that the substance has been decaying,
and m is the mass in grams that has
decayed.
If t > 0, what is the range of m?
Answer:
The range is 0 < m < 2000 when t > 0
Step-by-step explanation:
* Lets explain how to solve the problem
- The exponential function is , where
a is the initial amount and b is the growth factor
- If b > 1, then it is exponential growth function
- If 0 < b < 1, then it is exponential decay function
* Lets solve the problem
- A 2000 gram sample of radioactive matter will completely decay
(be undetectable) in 20 hours
- There is a set of ordered pairs (t , m) exists, where t is the amount
of time in hours that the substance has been decaying and m is
the mass in grams that has decayed
∵ We can represent this situation by an exponential decay function
∴ , where b is the growth factor which is
greater than zero and less than 1 , t is the lime in hours and
m(t) is the mass of the substance in gram
- In any function the domain is the value of x and the range is
the value of y
∵ In the function the domain is t and the range is m
∵ When t = 0 then m = 2000 ⇒ initial amount
∵ When t = 20 then m will be closed to zero
∴ The domain of the function is 0 < t < 20
∴ The range of the function is 0 < m < 2000
* The range is 0 < m < 2000 when t > 0
Whole numbers are the numbers 0, 1, 2, 3, 4, 5, 6...and so on. It is easier to compare two numbers through the millions using a place value chart. This is illustrated in the Figure bellow. In that example, we have chosen two numbers:
Number one:8,472,102
Number two:8,470,443
So, by comparing these numbers we will have the following steps:
Step 1. The millions are both 8.
Step 2. The hundred thousands are both 4.
Step 3. The ten thousands are both 7.
Step 4. The one thousands digits are 2 and 0.
Stop in this step and compare the digits, so:
2 is greater than 0 or 2 > 0
Therefore, the solution is:
Number one > Number two, that is:
8,472,102 > 8,470,443
In conclusion, you need to stop in the step at which the digits are not the same and compare them. The greatest number is the one with the greatest digit.