Question

(1) A toy truck travels at a rate of 0.5t ft/sec after t seconds of travel (so after 6 seconds the truck is traveling 3 ft/sec).

a) Graph the speed of the truck vs. time for 0<t<10.

b) Find the distance the truck has traveled in the first t seconds for 0<t<10. Call it T(t).

c) Find T'(5)

(2) A micorgram of Magnesium 28 contains approximately 3*10^16 atoms and this isotope has a half life of 21 hours.

a) Express the number of atoms of Magnesium 28 as a function of t, time in hours.

b) Approximately how many atoms of Magnesium 28 decay in the one second after 5 hours have passed? (Hint: what is the matematical relation for the decay as related to the amount?)