MATH SOLVE

4 months ago

Q:
# A 2000 gram sample of radioactivematter will completely decay (beundetectable) in 20 hours. Thereexists a set of ordered pairs (t, m),where t is the amount of time in hoursthat the substance has been decaying,and m is the mass in grams that hasdecayed.If t > 0, what is the range of m?

Accepted Solution

A:

Answer:The range is 0 < m < 2000 when t > 0Step-by-step explanation:* Lets explain how to solve the problem- The exponential function is [tex]f(x)= a(b)^{x}[/tex] , 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∴ [tex]m(t)= 2000(b)^{t}[/tex] , 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