If the original quantity is 14 and the new quantity is 22, which of these is the best estimate for the percent of change?
1 answer:
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Answer:
(a) n(t) = P(0)*e^(0.010939940t)
(b) 12,674,681 (nearest unit)
(c) 14 years (nearest year)
Step-by-step explanation:
rate = 1.1% / year = 1.011
(a)
P(0) = 12,000,000 = population in 2010
In compound interest format, after t years
P(t) = P(0)* (1.011)^t
Given format = P(0)* e^(rt)
therefore
e^(rt) = 1.011^t use law of exponents
(e^r)^t = 1.011^t
e^r = 1.011
r = log_e(1.011) = 0.010939940 (to 9 decimal places)
required formula is
n(t) = P(0)*e^(0.010939940t)
(b)
in 2015,
P(0)=12000000, n = 5 (years after 2010)
n(5) = 12000000*e^( 0.010939940 * 5 ) = 12,674,680.6 = 12,674,681 (nearest unit)
(c)
to reach 14 million, we equate
n(t) = 14,000,000
12,000,000 *e^(0.010939940*t) = 14,000,000
e^(0.010939940*t) = 14000000/12000000 = 7/6
take log on both sides
0.010939940*t = log(7/6)
t = log(7/6) / 0.010939940 = 14.091 years = 14 years to the nearest year.
See graph attached. Y-axis is in millions, x-axis is in years.
1-
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1 cm = 0.3937 inch
so, 91 cm = 91* 0.3937 = 35.826 inches
1 day = 24 hours
In 24 hours the bamboo grows = 35.826 inches
In one hour it will grow =
= 1.492 inches per hour. Hence the bamboo grows 1.492 inches per hour.
2-
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1 hour = 60 minutes
so 10 hours = 60 * 10 = 600 minutes.
60 seconds = 1 minute
so 24 seconds = = 0.4 minutes.
Now we have been given the total time as 10 hours, 39 minutes and 24 seconds
So adding all values in minutes, we get
600 + 39 + 0.4 = 639.4 minutes
So Saturn takes 639.4 minutes to complete one rotation
3-
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0.4(30h) represents the amount of tax Kimberly has to pay.