2. Larry has spent the last two years learning Spanish at the Academy of Foreign Languages. He noticed that the number of words in Spanish St) he
knows is given by the formula S (t) = a log(80t + 10) - 200 where a is a positive constant and t is the number of years after he registered in the
Academy.
a. At the end of his first year in the Academy, Larry knew 300 words in Spanish. What is the exact value of a? Show all your work.
b. Before entering the Academy, Larry knew some words in Spanish. How many new words has Larry learned in the Academy during the first two
wears? Shown all vour work
c. Assume Larry stary in the Academy and he keeps learing new words in Spanish according to the function S(t). How many years does he have to stay in the Academy in order to know 500 words in Spanish? Round your answer to the nearest 0.01 vear. Show all your work