<p>Hi everyone. As my SAT is few days away I’ve been cramming a lot 
</p>
<p>One math question came across and I honestly don’t know how to solve without a calculator. </p>
<p>The cost, in dollars, of production for u units at Max’s factory is expressed by the function P(u) = 3500(6/5)^u. If Max can spend $7300 on production, what is the maximum number of units he can produce? </p>
<p>a)0
b)1
c)2
d)3
e)4</p>
<p>Thank you guys in advance :)</p>
<p>I would convert 6/5 into a decimal personally then substitute in for u to find a number near 7300. Unless you can multiply fast in your head it would be hard to do without a calc. However 7300 is a little more than double 3500, so if you could plug in a u that would make 6/5 a little more than 2, like 1.20^4 then it should be it.</p>
<p>With a graphing calculator is easy: define P(u) := 3500(6/5)^u on your calculator and plug in P(1), P(2) etc. to find the max. u such that P(u) <= 7300. f(4) = 7257.6, so 4 is the answer.</p>
<p>Otherwise, we can find u such that P(u) = 7300 (u may not be an integer), and find floor(u) since P(u) is strictly increasing. Solving, we get u = log_(6/5) (7300/3500) which is about 4.03, so 4 is the answer. Either way, it’d be a bit time-consuming without a calculator.</p>