# Calculus

a certain radioactive substance is decaying so that at time t, measured in years, the amount of the substance, in grams, is given by the function f(t)=3e^-3t. What is the rate of decay of the substance after half a year:

I first found the derivative of f(t)=3e^-3t which is f'(t)=-9e^-3t. Then half a year would be 365/2 which is 182.5 days. When I substitute that in for t, i would get an answer of 0. What am i doing wrong?

1. 👍
2. 👎
3. 👁
1. Why are you using days when t was defined in years
so t = 1/2
f ' (1/2) = -9 e^(-3(1/2))
= -9 e^(-1.5)
= appr -2.008

1. 👍
2. 👎
2. Ah i see thanks!

1. 👍
2. 👎

## Similar Questions

1. ### math

An element has a half-life of 30 years. If 1.0 mg of this element decays over a period of 90 years, how many mg of this element would remain? Begin amount is 1.0 elapsed time is 90y half life 30 years n=9/30 n=3 90/2^2 90/8 =

2. ### calculus

A sample of a radioactive substance decayed to 94.5% of its original amount after a year. (Round your answers to two decimal places.) (a) What is the half-life of the substance? (b) How long would it take the sample to decay to

3. ### Exponential Modeling

The half-life of a radioactive substance is one day, meaning that every day half of the substance has decayed. Suppose you have 100 grams of this substance. How many grams of the substance would be left after a week?

4. ### AP science

You have 180 g of a radioactive substance. It has a half-life of 265 years. After 1,325 years, what mass remains?

1. ### 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

2. ### Calculus

The radioactive element polonium decays according to the law given below where Q0 is the initial amount and the time t is measured in days. Q(t) = Q0 · 2-(t/140) If the amount of polonium left after 700 days is 45 mg, what was

3. ### algebra

A radioactive substance decays according to the formula A=A0e^kt where A0 is the initial amount of substance (in grams) A is the amount of substance(in grams) after t years k is a constant The half-life of the substance is 10

4. ### ap calculus

suppose that the amount in grams of a radioactive substance present at time t (in years) is given by A (t) = 160e-.70t. Find the rate of decay of the quantity present at the time when t = 4

1. ### Calc

A sample of a radioactive substance decayed to 93.5% of its original amount after a year. a) What is the half-life of the substance? ? years (b) How long would it take the sample to decay to 10% of its original amount? ? years

2. ### precalculus

Twenty percent of a radioactive substance decays in ten years. By what percent does the substance decay each year?

3. ### Pre-calculus

Trtitum, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an into tail amount sample of 50 grams, how much will remain after 10 years?

4. ### Math

A radioactive substance decays exponentially. A scientist begins with 130 milligrams of a radioactive substance. After 20 hours, 65 mg of the substance remains. How many milligrams will remain after 24 hours?