Question

5. The half-life of a certain radioactive material is 78 hours. An initial amount of the material has

a mass of 790 kg. Write an exponential function that models the decay of this material. Find
how much radioactive material remains after 18 hours. Round your
answer to the nearest
thousandth.

Answer 1

395 = 790e^(k*78)

Explanation:

Dividing by 790 and taking the natural log

ln ( 395/790 ) = ( kx78 )

-0.6931 = 78k

-0.00888 = k

Now calculate how much is left after 18 hours:

Amount ( 18 )

= 790e^( -0.00888x18 )

Amount = 673.301 kg