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statuscvo [17]
3 years ago
15

Ted invests $8,310 in a savings account with a fixed annual interest rate of 2% compounded continuously. How long will it take f

or the account balance to reach it take for the account balance to reach $9,751.88?
Mathematics
1 answer:
Vsevolod [243]3 years ago
8 0

Answer: It will take 8 years.

Step-by-step explanation:

Equation for interest compounded continuously:

A=Pe^{rt} , A = accumulated amount , P=Principal value , r =rate of interest , t= time.

Given: P=  $8,310 , r = 2%  , A= $9,751.88

9751.88=8310e^{0.02t}\\\\\Rightarrow\ \dfrac{9751.88}{8310}=e^{0.02t}\\\\\Rightarrow\ 1.17351143201=e^{0.02t}

Taking natural log on both sides

\ln (1.17351143201)=\ln (e^{0.02t})\\\\\Rightarrow\ 0.160000478068=0.02t\\\\\Rightarrow\ t=\dfrac{0.160000478068}{0.02}\\\\\Rightarrow\ t=8.0000239034\approx8

Hence, it will take 8 years.

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3 years ago
One member of the debate team is going to be chosen president. each member is equally likely to be chosen. the probability that
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Let
x-------> <span>the probability that a boy is chosen
B------> </span>number of boys in the debate team
G------> number of girls in the debate team<span>

we know that
B+G=20-----> G=20-B-----> equation 1
</span>probability that a boy is chosen=number of boys in the debate team/total of people
so
x=B/20-------> equation 2

t<span>he probability that a girl is chosen is 2/3 the probability that a boy is chosen
</span>probability that a girl is chosen=(2/3)*x
probability that a girl is chosen=G/20
(2/3)*x=G/20-----> equation 3
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x=B/20
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using a graph tool
see the attached figure
the solution is
x=0.6
B=12
G=20-12-----> G=8

number of boys in the debate team is 12
number of girls in the debate team is 8
the probability that a boy is chosen is 0.6 ----> 60%
the probability that a girl is chosen is 0.6*(2/3)----> 0.4---> 40%

the answer is
number of girls in the debate team is 8

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