Question

This is a multiple choice question. A certain radioactive substance is decaying so that at time t, measured in years, the amount of the substance, in grams, is given by the function f(t)=-e^t +10. what is the rate of decay of the substance after 1 year?

the choice are
a) -3 g/year
b) -ln 2 g/year
c) -2.72 g/year
d)-1.53 g/year

Answer 1

C.

Explanation:

If the amount of substance left is given by `f(t)=-e^t+10,` the rate of decay will be given by the first derivative of that function.

So, find the first derivative, recalling that the derivative of the natural exponential function `e^t` is just itself, and that the `10,` a constant, goes away, as the derivative of a constant is zero.

`f'(t)=-e^t` (Units: g/year)

To determine the rate of decay after `1` year, evaluate the derivative at `t=1:`

`f'(1)=-e^1approx-2.72` g/year

The correct answer is C.