Answer: f(3)
Step-by-step explanation:
First find the formula for the rate of change by taking the derivative of 2^x. Let f(x) equal some hypothetical y-value, then take the natural log of both sides.
Implicitly differentiate the left side and take the derivative of the right side
Multiply both sides by 'y' which was defined as 2^x
Plug in x = 2 and x = 3 to see which slope is larger
Answer: choice A. 40 liters
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Explanation:
x = number of liters of the 50% alcohol solution
If we have x liters of 50% alcohol, then we have 0.50*x liters of pure alcohol. This is added to 0.90*40 = 36 liters of pure alcohol (from the 90% solution).
So far we have 0.50*x + 36. This expression represents the total amount of pure alcohol. We want a 70% solution, so we want 70% of the total 40+x meaning 0.50*x + 36 is to be set equal to 0.70*(40+x) and we solve for x as shown below
0.50*x + 36 = 0.70*(40+x)
0.50*x + 36 = 0.70*(40)+0.70*(x)
0.50*x + 36 = 28+0.70*x
36 - 28 = 0.70*x - 0.50x
8 = 0.20x
0.20x = 8
x = 8/0.20
x = 40
So that is why the answer is choice A. 40 liters
The son is 4 years old and the dad is 24 years old.
30% = .3
.3(24.40a + 14.50c)
24.40 = cost of adult ticket
14.50 = cost of child ticket
a = # of adult tickets sold
c = # of child tickets sold
.3 * 24.40a + .3 * 14.50c
answer: 7.32a + 4.35c
