Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.(1 - 
) (1 - 
) . . . (1 - 
) = 
What will be an ideal response?
First we show that the statement is true when n = 1.
For n = 1, we get 
= 
= 
.
This is a true statement and Condition I is satisfied.
Next, we assume the statement holds for some k. That is,
is true for some positive integer k.
We need to show that the statement holds for k + 1. That is, we need to show that
So we assume that (1 - 
) (1 - 
) . . . (1 - 
) = 
is true and multiply the next term, 
to both sides of the equation.
(1 - 
) (1 - 
) . . . (1 - 
)(1 - 
) = 
(1 - 
)
= 
- 
= 
- 
= 
= 
= 
Condition II is satisfied. As a result, the statement is true for all natural numbers n.
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Divide and write answer in lowest terms.
÷ 
A. 
B. 
C. 
D. 
Solve the problem.Kayla, a photographer, can produce prints of her photos at a cost of $3 per print, with a setup cost of $35 per run. She sells the prints for $9 each. Write an equation for the profit. Let P represent the profit and x represent the number of photos produced. Graph the equation by hand. Use the graph to determine the the number of prints produced and sold to obtain a profit of $0. 
A. P = 6x + 35; 6 prints
B. P = 9x + 35; 4 prints
C. P = 9x - 35; 4 prints
D. P = 6x - 35; 6 prints
Solve the problem.Suppose the algae growth in Black Oak Lake increased from 100,000 cells per milliliter to approximately 10,000,000 cells per milliliter in a 
period. The specific growth 
is defined by 
where N1 is the algae concentration at time x1 and N2 is the algae concentration at time x2. In this situation, what is the specific growth rate of algae? Round your results to the nearest hundredth.
A. -1,414,285.71 B. -0.29 C. 1,414,285.71 D. 0.29
?Find the second derivative for the function 
and solve the equation 
.
?
A. ?0
B. ?4
C. ?-4
D. ?
E. ?no solution