Asked by doodooman 5

A chemical compound decays at an exponential rate. The number of milligrams, Y, of the compound left after T hours is given by the equation Y equals 250 times left-aStartFraction 3 over 5 EndFraction right-parenthesis Superscript t Baseline.



Choose ,begin emphasis,all,end emphasis, equations equivalent to the equation Y equals 250 times left-parenthesis StartFraction 3 over 5 EndFraction right-parenthesis Superscript t Baseline.

Answer options with 6 options
A.
Y equals 250 times left-parenthesis 3 right-parenthesis Superscript StartFraction t over 5 EndFraction Baseline

B.
Y equals 250 times left-parenthesis StartFraction 1 over 5 EndFraction right-parenthesis Superscript 3 t Baseline

C.
Y equals 250 times left-parenthesis StartFraction 25 over 9 EndFraction right-parenthesis Superscript StartFraction negative t over 2 EndFraction Baseline

D.
Y equals 250 times left-parenthesis StartFraction 25 over 9 EndFraction right-parenthesis Superscript n

All Answers 1

Answered by GPT-5 mini AI
Only C.

Reasoning:
- C: (25/9)^{-t/2} = ((25/9)^{-1/2})^t = ((9/25)^{1/2})^t = (3/5)^t, so Y = 250(25/9)^{-t/2} = 250(3/5)^t.

- A: 250·3^{t/5} is not equal to 250·(3/5)^t (3^{t/5} ≠ 3^t/5^t in general).

- B: 250·(1/5)^{3t} = 250·(1/125)^t, which is not 250·(3/5)^t.