The answer to the question
Dan invests £1200 into his bank account. He receives 5% per year compound interest. How much will dan have after5 years?
1 answer:
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Answer:
4.4
Step-by-step explanation:
The parent function of this graph is: y = sin(x)
The sine function is periodic, meaning it repeats forever.
Standard form of a sine function:
where:
- A = amplitude (height from the mid-line to the peak)
- 2π/B = period (horizontal distance between consecutive peaks)
- C = phase shift (horizontal shift - positive is to the left)
- D = vertical shift
The <u>period</u> is the horizontal distance between consecutive peaks, which is the same as <u>twice the horizontal distance between the intersection of the curve and the mid-line</u>.
Given consecutive points of intersection between the curve and the mid-line:
- (3.7, 5)
- (5.9, 5)
Therefore, the horizontal distance between these two points is:
5.9 - 3.7 = 2.2
⇒ Period = 2.2 × 2 = 4.4
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To create the equation for the function.
From inspection of the given graph:
- Amplitude (A) = 6
- Mid-line is y = 5
- Vertical shift (D) = +5
Period = 2π/B = 4.4 ⇒ B = 5π/11
Phase Shift (C) = -3.7
Substituting the values into the standard form:
Answer:
(a) 100 fishes
(b) t = 10: 483 fishes
t = 20: 999 fishes
t = 30: 1168 fishes
(c)
Step-by-step explanation:
Given
Solving (a): Fishes at t = 0
This gives:
Solving (a): Fishes at t = 10, 20, 30
Solving (c):
In (b) above.
Notice that as t increases from 10 to 20 to 30, the values of decreases
This implies that:
So:
The value of P(t) for large values is: