Answer:
C(n) = 4 n for all possible integers n in N. This statement is true when n=1 and proving that the statement is true for n=k when given that statement is true for n= k-1
Step-by-step explanation:
Lets P (n) be the statement
C (n) = 4 n
if n =1
(x+4)n = (x+4)(1)=x+4
As we note that constant term is 4 C(n) = 4
4 n= 4 (1) =4
P(1) is true as C(n) = 4 n
when n=1
Let P (k-1)
C(k-1)=4(k-1)
we need to proof that p(k) is true
C(k) = C(k-1) +1)
=C(k-1)+C(1) x+4)n is linear
=4(k-1)+ C(1) P(k-1) is true
=4 k-4 +4 f(1)=4
=4 k
So p(k) is true
By the principle of mathematical induction, p(n) is true for all positive integers n
<span> the answer is 9 23/27
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Answer: in five years time, the sales would be $100367
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total sales at the end of t years
r represents the growth rate.
n represents the periodic interval at which it was compounded.
P represents the current sales.
t represents the time in years
From the information given,
P = 75000
r = 6% = 6/100 = 0.06
n = 11 because it was compounded once in a year.
t = 5 years
Therefore,
A = 75000(1+0.06/1)^1 × 5
A = 75000(1+0.06)^5
A = 75000(1.06)^5
A = $100367
(-8x) ÷ (-2)
= (-4x) ÷ (-1)
= 4x ÷ 1 = 4x
800 is linear and 500 is exponential
