Answer
$t = 9$ months
Work Step by Step
$$f(t) = 75 - 10\log(t+1)$$ To find the value of $t$ where the average score falls below 65, we can do the following: $$f(t) = 65 = 75-10\log(t+1)$$ $$-10 = -10\log(t+1)$$ $$1 = log_{10}(t+1)$$ $$10^1 = t+1$$ $$10-1 = 9 = t$$ By looking at the graph and drawing a line at $y=65$, we confirm this by noticing that the graph crosses it at around $x =9$, which is to say, $9$ months.