Question

Materials A and B decay over time. The function

for the amount of material A is A(t) = 1000(0.5) ²¹
and for the amount of material B is
B(t) = 1000(0.25)', where t represents time in days.
On which day will the amounts of material be
equal?
1) initial day, only 2) day 2, only 3) day 5,
only 4) every day

Answer 1

Explanation:

To find the day on which the amounts of materials A and B are equal, we need to set A(t) equal to B(t) and solve for t:

A(t) = B(t)

1000(0.5)^t = 1000(0.25)^t

0.5^t = 0.25^t

tlog(0.5) = tlog(0.25)

t = log(0.25)/log(0.5)

Using a calculator, we can evaluate this expression to be approximately 4.32 days.

Therefore, the amounts of materials A and B will be equal on day 4 or 5 (depending on how you define the "initial day"), but not on day 2 or every day.

So, the correct answer is option 3) day 5, only.