Question

A scientist measures the initial amount of Carbon-14 in a substance to be 25 grams.

The relationship between A, the amount of Carbon-14 remaining in that substance, in grams, and t, the elapsed
time, in years, since the initial measurement is modeled by the following equation.
A = 25e 0.00012
In how many years will the substance contain exactly 20 grams (g) of Carbon-14
Give an exact answer expressed as a natural logarithm.
years

Answer 1

To find the number of years it will take for the substance to contain exactly 20 grams of Carbon-14, we set up the equation 20 = 25e^(-0.00012t) and solve for t. The exact answer, expressed as a natural logarithm, is t = -ln(0.8) / 0.00012 years.

Step-by-step explanation:

The relationship between the amount of Carbon-14 remaining in a substance, A, and the elapsed time, t, since the initial measurement is given by the equation A = 25e^(-0.00012t), where e is the base of natural logarithms. We need to find the value of t when A is 20 grams.

To solve for t, we can set the equation equal to 20 and solve for t:
20 = 25e^(-0.00012t)

Divide both sides of the equation by 25:
0.8 = e^(-0.00012t)

To isolate t, take the natural logarithm of both sides of the equation:
ln(0.8) = -0.00012t

Finally, divide both sides of the equation by -0.00012 to solve for t:
t = -ln(0.8) / 0.00012

The exact answer to this equation, expressed as a natural logarithm, is t = -ln(0.8) / 0.00012 years.

Answer 2

In(0.8)/-0.00012