DF001
  • DF001
Suppose $5000 is invested at 7% interest compounded continuously. How long will it take for the investment to triple? Use the model a(t) = Pe^rt
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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DF001
  • DF001
\[A(t) = Pe ^{rt}\]
mathmale
  • mathmale
Good. That's the Amount formula for continuous compounding. What does the verb "tiple" mean?
DF001
  • DF001
How do I find t

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mathmale
  • mathmale
Again, please explain the meaning of "triple."
DF001
  • DF001
A(t)=5000*e^7%*t
DF001
  • DF001
triple = x3?
DF001
  • DF001
x3 of 5000?
mathmale
  • mathmale
3x, actually. In this problem, what "triples?"
DF001
  • DF001
the investment of $5,000?
mathmale
  • mathmale
Yes. if $5000 triples in value, what's the new value of your investment?
DF001
  • DF001
$15,000
mathmale
  • mathmale
Right. So, in the equation\[A=Pe ^{rt}, A has what\]
DF001
  • DF001
A(t)=$15,000
mathmale
  • mathmale
A has what value? P has what value? Note that r should not be expressed as a percentage (7%), but as a decimal fraction. Write the equation again, including the values of A, P and r.
DF001
  • DF001
|dw:1450110473900:dw|
mathmale
  • mathmale
Yes!\[3=e ^{0.07t}\]
mathmale
  • mathmale
How would you solve for t?
DF001
  • DF001
oh then ln3=lne^0.07t
mathmale
  • mathmale
Hint: which mathematical operation is the inverse of exponentiation?
mathmale
  • mathmale
Yes. Simplify that.
DF001
  • DF001
I see. thankss
mathmale
  • mathmale
You're welcome! Bye.

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