Question

Marie is logging the number of radioactive isotopes she observes every minute. She has determined her function to be f(x) = -4x + 120.
Based on the situation above, describe any necessary restrictions to the domain and range. Provide justification for the restrictions.

Answer 1

we can say that x >= 0, because f is a function of time, and i don't think there's a meaning for negative time in this context.

to find the time the substance is reduced to nothing (is 0) just solve for 0:
0=-4x + 120
and we find that at x=30minutes the value is 0

so [0,30] is the domain

Then when I'm thinking of the range, we can look at the function and see that it starts at a number, and reduces, so at minute 0, the value is 120. At the final minute, the value is 0.
So the rannge is [0,120]