A2000 gram sample of radioactive
matter will completely decay (be
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?

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