Pre-Cal half-lifes?

Question

The amount C in grams of carbon-14 present in a certain subsance after t years is given by

C= 20e^-0.0001216t

Estimate the half-life of carbon-14.

Answer 1

The formula for determining exponential decay is:
N(t) = No * e^(-λt)

To find the half life, set No = 1, and N(t) = .5.
.5 = e^-0.0001216t

Take ln of both sides to remove the exponent:
ln .5 = -0.0001216t
-0.693 = -0.0001216t
5699 = t

This answer is within the actual half life: 5730±40 years.

Answer 2

y = Ce^(kt) y is very final mass, C is preliminary mass, ok is the relative decay element, t is time (2.) a million/2 = e^(1590k) ln(a million/2) = 1590k ok = ln(a million/2)/1590 ok ? -0.000436 once you're employing a calculator, shop employing this spectacular type. Rounding this early could make your very final answer off via some extra digits. y = 100e^(ok(2000)) y = 100e^(2000 ln(a million/2)/1590) y ? 40-one.816 mg ------------------------ (3.) a million/2 = e^(4k) ln(a million/2) = 4k ok = ln(a million/2)/4 ok ? -0.173 4 = Ce^(12k) C = 4/(e^(12k)) C = 32 mg After 5 weeks: 5 weeks = 35 days (you ought to replace to days using fact the 0.5-existence is in this unit.) y = 32e^(35k) y = 32e^(35*ln(a million/2)/4) y ? 0.0743 mg