Question

Cesium-137 is a radioactive isotope with a variety of industrial and medical applications, known for its relatively long half-life of about 30 years. It has been observed that the activity of the sample decreases by 2.3% each year. This decay can be represented by the recursive equation
B
(
x
)
≈
B
(
x
−
1
)
⋅
0.977
, in which
B
(
x
)
is the activity in millicuries after x years, and
B
(
0
)
=
15
mCi. Create an exponential equation that models the decay of cesium-137 in the sample over time. Round your answer to four decimal places. Which of the following is the correct equation?(1 point)

B
=
15
e
−
0.0221
t

B
=
15
(
0.9770
)
t

B
=
15
e
−
0.0233
t

B
=
15
e
−
0.0230
t

Answer 1

B(x) = 15(0.9770)^x.

(Equivalently, B(x) = 15 e^{x ln(0.977)} = 15 e^{-0.0233 x}, since ln(0.977) ≈ -0.0232686 ≈ -0.0233.)