Math word problem help

Question

Prehistoric cave painting were discovered. The paint contained 5% of the original carbon-14. Estimate the age of the paintings using the exponential decay model for carbon-14, A=A₀e ^-0.000121t (round to the nearest whole number as needed.)

 

The paintings are approximately ? years old.

Answer 1

A = current amount

A₀ = original amount

 

0.05 A₀ = A

A = A₀ e^-0.000121t

A / A₀ = e^-0.000121t

0.05 = e^-0.000121t

ln 0.05 = ln e^-0.000121t

ln 0.05 = -0.000121t ln e

ln 0.05 = -0.000121t

-2.9957 ≈ -0.000121t

24758.11 ≈ t

 

The cave paintings are approximately twenty-four thousand seven hundred fifty-eight years old.