If f(x) is an exponential function where f(-1.5) = 27 and f(7) = 83, then find the value of f(-0.5), to the nearest hundredth.

Quick translate "x is 12 units from 20" into an equation. what are the values of x being described? if you can answer any of my other questions that'd be great too

What is the value of x in the equation (2)3) (x+6)= -18 a. -36 b. -33 c. -24 d. -18

If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is a(x) = p(x) x . (a) find a'(x). a'(x) = xp'(x) − p(x) x a'(x) = xp'(x) − p(x) x2 a'(x) = p'(x) − p(x) x a'(x) = xp'(x) − p'(x) x2 a'(x) = p'(x) − xp(x) x2 why does the company want to hire more workers if a'(x) > 0? a'(x) > 0 ⇒ a(x) is ; that is, the average productivity as the size of the workforce increases. (b) if p'(x) is greater than the average productivity, which of the following must be true? p'(x) − xp(x) > 0 p'(x) − xp(x) < 0 xp'(x) − p'(x) > 0 xp'(x) − p(x) < 0 xp'(x) − p(x) > 0