Exponential Modelling Question

Question

Radium has a half-life of 1620 years. Suppose 3 g of radium is present initially. Complete the table. (Round ALL decimal answers to the nearest hundredth  EXCEPT  your answer for b which will need to be rounded to 4 decimal places.  Do NOT write decimals after whole numbers. For example, enter the whole number 3 as just 3 and not 3.00.)

First Second Third Fourth

T 0 1620 Answer Answer

f(t) 3 Answer Answer Answer

 Give an exponential model for the amount of radium left as a function of time t:  f(t) = Answer(answer)^t

Estimate how much radium would remain after 4000 years: Answer

Answer 1

Hi, Mike,

I don't clearly understand the table. Do the words "Second, Third, and Fourth" refer to the number of half-lives?

If so, the amount left can be shown as the following table:

The formula for amount remaining is:

N(t) = No(1/2)^t/th where

n(t) is amount remaining,

No is the initial amount

t is the time elapsed, and

th is the half life.

I see that you are not supposed to write any decimals after the whole numbers, which is another reason I don't understand the question. If so, the answers would be 3, 1, 0, 0, 0. Makes no sense to me, so I must be reading the problem incorrectly.

Bob