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 [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
