Unformatted text preview: 3.3 dark
d‘t =2A Emit): ce'2t I Suppose that PD is invested in a savings account in which interest is compounded continuously
at 72% per year. That is, the balance P grows at the rate given by the following equation. d—p — 0072p:
dt — O (a)Fi.nd the function 13(t) that satisﬁes the equation. Write it in terms of PD and 0.072. (b)Suppose that $1000 is invested. 1What is the balance aﬁer 1 years?
(c)When will an investment of $1000 double itself? (a) Choose the correct answer below.
a» 130:): 130600321
13(t) = 130319972"
P0 = 130030.072: P(t)=0.072PUet (b) The balance aﬁer 1 yearis $ 1074.66.
(Type an integer or decimal rounded to two decimal places as needed.) I’cl "Tie rlnul'ilina time is 9 ﬁ? vear _ _ _ _ _ _ _
How many years are required for an investment to double in value if it is appreciating at the rate of 2% compounded continuously? At 2% compounded continuously, the investment doubles in 34.? years. Initial Deposit ﬁrmual Rate Doubling Time ﬁmount in 30
($3 (9/0} (Fr) Fr ($3
1000 77 Initial Deposit Annual Rate Doubling Time Arnolmt in 30 '3) (9’3) (Fr) Fr ($3 1000 77 9.0 100721.42
In 2004, an art collector paid $5?,?43,000 for a particular painting. The same painting sold for
$2?,000 in 1950. Complete parts (a) through a) Find the exponential growth rate k, to three decimal places, and determine the exponential
growth function V, for which Vlth is the painting's value, in dollars, tyears after 1950. 1:: 0.142
(D0 not round until the ﬁnal answer. Then round to three decimal places as needed.) Choose the correct answer below. " Wt) 47,0002 9142*
b) Predict the value ofthe painting in 2010. $ 135,379,000
(Do not round until the ﬁnal answer. Then round to the nearest thousand as needed.) c) VJhat is the doubling time for the value of the painting? 4.9 yr
(Do not round until the ﬁna. answer. Then round to the nearest tenth as needed.) d) How long aﬁer 1950 wil. the value of the painting be $1 billion? 74 yr
Suppose that in 1611, a man bought a diamond for $11. Suppose that the man had instead put
the $1 1 in the bank at 4% interest compounded continuously. Iﬁfhat would that $11 have been
worth in 2005? In 2005, the $11 would have been worth approximately $ T6890683. a) TWhat percentage buy the game without seeing a TV ad (X: D)? 2 %
(Type an integer or a decimal rounded to the nearest tenth as needed.) b) mat percentage buy the game after the ad is run 36 times? 36.4 %
(Type an integer or a deciInal rounded to the nearest tenth as needed.) c) Find the rate of change, P '(X). EDDIE 43.16::
(1+ 5'] IE, D.15x:2
57%] 1+ 4.7'3 e "14* P '(X) =
PU?) =
a) Find the population after 17" years. 5T4? (Round to the nearest integer as needed.) b) Find the rate of change, P '(t). 21523.40'04t " 11,051.35; "14*
(1+ wane '5'“)? (1+4_T8.=3 "1“)?
{1+4.T8e '0‘“)? 21628.4D'D'4t , . 2 ' + . 2 '
1105136 ‘0‘“ 1 47's ‘0‘“ 2 P13): 1oo{1— e ‘04“)
a) TNhat percentage of doctors are prescribing the medication after 6 months? 91. 5 %
(Do not round until the ﬁnal answer. Then round to the nearest tenth as needed.) b) Find P '05), and interpret its meaning. P16) = 3.5
(Do not round until the ﬁnal answer. Then round to the nearest tenth as needed.) Choose the correct interpretation below. '’ At 6 months, the percentage of doctors who are prescribing the medication is
increasing by 3. 5% per month. ...
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 Spring '11
 JoyceRosebergh
 $2, $3, $5, 4%, EDDIE 43.16

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