Answer:
21. y = 75000·0.935^t
22. after 74.6 days
23. y = 27.8112·1.18832^t
24. 18.8% per month
25. 1748
Step-by-step explanation:
22. It is convenient to use the graphing calculator to solve this problem. The number of days is where the exponential curve has the value 500. It is about 74.55 days. (see the first attachment)
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23. y = 27.8112·1.18832^t (see the second attachment)
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24. The rate of change is the difference between the base of the exponential and 1, often expressed as a percentage. The time period is the units of t.
(1.18832 -1) × 100% ≈ 18.8% . . . . per month
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25. Evaluating the function for t=24 gives y ≈ 1748.30425259 ≈ 1748.
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<em>Comment on graphing calculator</em>
A graphing calculator can make very short work of problems like these. It is worthwhile to get to know how to use one well.
Answer:
17.5
Step-by-step explanation:
Given that the variables x and y have a proportional relationship.
i.e. y is directly proportional to x or can be written as
y = mx where m is the constant of proportionality.
When x =2, y =7
Substitute this to get the value of m.
7 =2m or m = 3.5
Thus the relationship between x and y is
y = 3.5x
So when x=5, y = 3.5(5) = 17.5
Answer: C. (-7x+9)(x-2)
Step-by-step explanation:
1. Factor out the negative sign.
−(7x^2+5x−18)
2. Split the second term in 7x2+5x−18 into two terms.
−(7x^2+14x−9x−18)
3, Factor out common terms in the first two terms, then in the last two terms.
−(7x(x+2)−9(x+2))
4. Factor out the common term x+2x+2x+2.
−(x+2)(7x−9) or (-7x+9)(x-2)