Question

The expression
500
(
0.5
)
(
t
5730
)
represents the number of grams of the isotope Carbon-
14
after
t
years in a rock. Jayden claims that the initial amount the isotope is
500
grams and the expression represents exponential growth.



Which TWO statements BEST evaluate Jayden's claims?



A.
The initial amount is
500
grams since this is the value of the expression when
t
=
0
.

B.
The initial amount is
500
grams since this is the value of the expression when
t
=
1
.

C.
The expression represents exponential decay because the value inside the parentheses is less than
1
.

D.
The expression represents exponential growth because the value inside the parentheses is less than
1
.

E.
The initial amount is
5730
grams since it is part of the exponent for the exponential expression.

Answer 1

Correct choices: A and C.

- A is true: when t = 0 the expression is 500(0.5)^(0) = 500, so the initial amount is 500 g.
- C is true: the base 0.5 is less than 1, so the quantity decreases over time — this is exponential decay, not growth.

B, D, and E are incorrect.