Part b.
This function represents a decay. Thus the values of A(t) must decrease with the increase of time t.
So, only graphs C and D are eligible answers.
Also, we are informed that the initial amount present is 800g, which can be obtained when making t = 0 in the expression that defines the function.
Therefore, for t = 0, we must have A(t) = 800. This means the graph crosses the vertical axis at A(t) = 800.
Thus, only option C is correct:
In order to know the half-life of this isotope, we can identify the point on the graph for which
A(t) = A(0)/2 = 800/2 = 400
Observing the graph, we can see that this happens for t between 20 and 30 years, but closer to 20:
Therefore, estimating the half-life of this isotope, the only possible answer is:
about 24.03 years (option C)