[Video] Q38: The penicillin concentration, in micrograms per milliliter, in the patient’s bloodstream t minutes after the penicillin injection is modeled by the function p defined by p(t) = 200b^t/5. if p approximates the values in the table to within 10 micrograms per milliliter, what is the value of b, rounded to the nearest tenth?

Explanation for Question 38 From the Math (Calc) Section on the Official Sat Practice Test 8

So number 38, we're given a function for P of T and were told 2 to solve for B. So we have PFT is equal to 200 times B 3 raised to the T over five. What we notice about this equation is that 4 there's three variables in play. There's a PFT there's B, 5 which we want to solve for. And then there's T so if we want 6 to solve for B, we need to find a value for PFT to plug 7 in and we need a value of T to plug in. 8 And the place that we get, those values is up here in our graph. 9 Cause if we look at our X axis, we see that we have T 10 time. If we look at our Y axis, 11 we see that we have penicillin concentration, 12 which we're told is PFT. 13 So any EXCOM of Y point is actually a T comma P of T 14 point. 15 And then we can take those values and plug them into our equation. 16 So for example, we can take this point here at five comma, 17 one 50, and now get a value of T that's five and a PFT. 18 That's one 50 and plug those into our equation. 19 So instead of writing, PFT I'll write one 50 is equal to a hundred 20 times B, I'm still solving for B. I don't have any value to put 21 there. And then if T I'll put five, 22 because I was at five on my X axis. 23 And so now everything has been plugged in for except B. 24 And I can, I can officially solve for B here. 25 So this five over five will simplify to just one. 26 So if one 50 is equal to 200 times B to the one or 27 just 200 times B cause expo of one, 28 isn't really necessary to write and I can divide by 200 to 29 get beyon...