When will the population double from its size at t = 0  TOPIC_SOLVED

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When will the population double from its size at t = 0

Postby hbelle on Fri May 28, 2010 2:14 am

The population of a city (in millions) at time t (in years) is given by the formula below, where t = 0 is the year 2000.
P(t) = 2.5e^0.03t
When will the population double from its size at t = 0? (Round to two decimal places.)
t =
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Postby maggiemagnet on Fri May 28, 2010 11:17 am

hbelle wrote:The population of a city (in millions) at time t (in years) is given by the formula below, where t = 0 is the year 2000. P(t) = 2.5e^0.03t When will the population double from its size at t = 0? (Round to two decimal places.)

What is the population at in 2000? (Hint: Plug in the given value, and simplify.)

What will the doubled value be? (Hint: Multiply by 2.)

At what value of t will P(t) take on this doubled value? (Hint: Plug doubled value in place of "P(t)", and solve the resulting exponential equation.)

:wink:
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Re: When will the population double from its size at t = 0  TOPIC_SOLVED

Postby hbelle on Fri May 28, 2010 2:02 pm

Thank you maggiemagnet. I appreciate the hints so does this following sense?

What is the population at in 2000?
P(0) = 2.5e^0.03(0)
P(0) = 2.5e^0 ............ e^0 = 1 so
P(0) = 2.5

What will the doubled value be?
2(2.5) = = 2.5e^0.03t
2 = e^0.03t
ln 2 = 0.03t
ln 2 /0.03 = t
t = 23.1049 so the population would be doubled in 23.10 years? (2023)
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Re: When will the population double from its size at t = 0

Postby maggiemagnet on Fri May 28, 2010 11:18 pm

Looks good to me! :thumb:
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