F(x) is continuous for all x.
Pick a point and show that f(x) is either negative or positive. Pick another point and show that f(x) is negative, if positive, or positive, if negative.
At x = 30, f(30) - 1000 = 900 + 10sin(30) - 1000 ≤ 0
Now, show at another point f(x) - 1000 is positive, and hence, there would be root between 30 and such point.
Let's pick 40.
At x = 40, f(40) - 1000 = 1600 + 10sin(40) - 1000 ≥ 0
Since f(x) - 1000 is continuous, there lies a root between 30 and 40, and hence, 30 ≤ c ≤ 40
The general way to work this out is to solve the general expression for
the remaining quantity versus half-life, using logarithms. But that's not
necessary with these numbers.
Look at the numbers:
-- 3 mg is 1/4 of 12 mg.
-- 1/4 is the product of (1/2) x (1/2).
-- So the 3 mg is what's left of 12 mg after 2 half-lives.
The 26 minutes must be two half-lives.
-- The half-life of that substance is 26/2 = <em>13 minutes</em>.
Go Maggie !
-2x = -1
x = 1/2
Any equation that returns x=1/2 is a solution to this problem. For example, x= (3•4)/6 can be simplified so that x=1/2
13.5/3 = 4.5
He hiked for 4.5 hours.
