Use mathematical induction to prove the statement is true for all positive integers n.2n > 2n-1
What will be an ideal response?
Answers may vary. Possible answer:
First, we show the statement is true when n = 1.
For n = 1, 21 > 21-1.
Since 21-1 = 20 = 1 and 21 > 1, P1 is true and the first condition for the principle of induction is satisfied.
Next, we assume the statement holds for some unspecified natural number k. That is,
Pk: 2k > 2k-1 is assumed true.
On the basis of the assumption that Pk is true, we need to show that Pk+1 is true.
Pk+1: 2k+1 > 2k
So we assume that 
is true and multiply both sides of the equation by 2
2k? 2 > 2k-1? 2
2k+1 > 2(k-1)+1
2k+1 > 2k
So Pk+1 is true if Pk is assumed true. Therefore, by the principle of mathematical induction, 
for all natural numbers n.
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Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing.y = - 
A. Increasing -? < x < 0 and 0 < x < ?
B. Increasing -? < x < 0
Decreasing 0 < x < ?
C. Decreasing -? < x < 0 and 0 < x < ?
D. Decreasing -? < x < 0
Increasing 0 < x < ?
Solve the exponential equation and approximate the result, correct to three decimal places.(3.1)x = 45
A. 3.3523 B. 3.488 C. 3.3769 D. 3.3646
Refer to the equation 3x- 2y = -6. Write the equation in slope-intercept form.
What will be an ideal response?
Perform the indicated operations and simplify the result. Leave the answer in factored form.
+ 
A. 
B. 
C. 
D. 