# Pre Calculus

posted by .

Exponential Growth and Decay

Find the half-life of a radioactive substance that decays by 5% in 9 years.

• Pre Calculus -

x = xi e^-kt
.95 = e^-9 k
ln .95 = -9k
k = .005699

.5 = e^-.005699 t
ln .5 = - .005699 t
t = 121.6 years

## Similar Questions

1. ### calculus

Carbon-14 is a radioactive substance produced in the Earth's atmosphere and then absorbed by plants and animals on the surface of the earth. It has a half-life (the time it takes for half the amount of a sample to decay) of approximately …
2. ### Pre Calculus

Exponential growth and decay find the half life of a radioactive substance if 220 grams of the substance decays to 200 grams in 4 years?
3. ### Science

Radioactive substance decays so that after t years, the amount remaining, expressed as a percent of the original amount, is A(t)=100(1.6)^(-t). a) Determine the function A’, which represent the rate of decay of the substance. b) …
4. ### calculus

The rate at which an amount of a radioactive substance decays is modeled by the differential equation dA/dt = kA, where A is the mass in grams, t is the time in years, and k is a constant. Answer the following. a) If a 100-gram sample …
5. ### Math

A radioactive substance decays according to the formula Q(t) = Q0e−kt where Q(t) denotes the amount of the substance present at time t (measured in years), Q0 denotes the amount of the substance present initially, and k (a positive …
6. ### Math

A radioactive substance decays according to the formula Q(t) = Q0e−kt where Q(t) denotes the amount of the substance present at time t (measured in years), Q0 denotes the amount of the substance present initially, and k (a positive …
7. ### Math-Exponential Decay

A lab technician had 58 grams of a radioactive substance. Ten days later, only 52 grams remained. Find the half-life of the radioactive substance.
8. ### Exponential decay

Show that if a radioactive substance has a half life of T, then the corresponding exponential decay function can be written as y=y0e^kt
9. ### Pre Calculus 1

thirty percent of a radioactive substance decays in four years. assuming the decay is exponential, find the half life of the substance. the beginning of 1975 the population of a country was 40 million and growing at a rate of 3% per …
10. ### Calculus

The rate of decay is proportional to the mass for radioactive material. For a certain radioactive isotope, this rate of decay is given by the differential equation dm/dt = -.022m, where m is the mass of the isotope in mg and t is the …

More Similar Questions