The amount a in grams of a radio, active material that is sticking can be modeled by A(d)=450(0.88)^x where deer is the number of days since it started it’s decay. Give an interpretation of the fact that A(14)=75.

Question

A) in 75 days there is 14 g of the radioactive material left
B) in 14 days there is 75 g of radioactive material left
C) in 450 days there is 75 g of the radioactive material left
D) in 88 days there is 14 g of the radioactive material left

Answer 1

The expression \( A(d) = 450(0.88)^x \) models the amount of radioactive material remaining after a certain number of days, \( x \). When we evaluate \( A(14) \), we are finding the amount of material left after 14 days.

To find \( A(14) \):

\[ A(14) = 450(0.88)^{14} \]

The interpretation of the statement \( A(14) = 75 \) is that after 14 days, there are 75 grams of the radioactive material left.

Therefore, the correct interpretation is:

B) in 14 days there is 75 g of radioactive material left.