Aradioactive substance has a decay rate of 5% per hour. if 500 hundred grams are present initially, how much of the substance remains after 4 hours?

First we have to calculate the half-life
half-life = elapsed time * log (2) / log (bgn amt / end amt)
half-life = 1 hour * 0.30102999566 / log (1 / .95)
half-life = 0.30102999566 / log ( 1.0526315789 )
half-life = 0.30102999566 / 0.022276394692
half-life =  13.5134073454 hours

Ending Amount = Beginning Amount / 2^n
Where "n" = number of half-lives
For 4 hours, "n" equals
4 / 13.5134073454
= 0.2960023255

Ending Amount = 500 grams / 2^.2960023255
Ending Amount = 500 grams / 1.2277376629
Ending Amount =  407.2531250707 grams

Source:
http://www.1728.org/halflife.htm

Hello!

the answer is:

the correct option:

b.

why?

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!