Question

exploration 3.2.1 you used exponential and logarithmic expressions to learn about carbon dating. in question 5, the general equation for half-life of carbon-14 is . how might this equation change for radium which has a half-life of 2600 years?

Answer 1

The general half-life equation for carbon dating is adapted for Radium by changing the half-life value in the exponent to Radium's half-life of 2600 years, resulting in the equation Nt = N0(1/2
`)^(t/2600)`. Option D is correct.

The general equation for carbon-14 dating based on half-life is expressed as Nt = N0(1/2
`)^(t/5730)` where t is the time in years, N0 is the initial number of nuclei, and Nt is the number of nuclei after time t.

For Radium with a half-life of 2600 years, this equation would be modified to Nt = N0(1/2
`)^(t/2600)`, which matches option D. The key modification is to replace the original half-life of carbon-14 (5730 years) with the half-life of Radium (2600 years) in the exponent of the equation.

Hence, D. is the correct option.

--The given question is incomplete, the complete question is

"In Exploration 3.2.1 you used exponential and logarithmic expressions to learn about carbon dating. In question 5, the general equation for half-life of carbon-14 is N_t=N_0( 1/2 )^ t/5700 . How might this equation change for Radium which has a half-life of 2600 years? A) N_t=N_0( 1/2 )^ 2600/h B) N_t=N_0( 1/2 )^ 2600/5700 C) N_t=2600( 1/2 )^ t/5700 D) N_t=N_0( 1/2 )^ t/2600."--