SOLUTION: The population of a town is 10,000 people. The population is growing according to the function P(t) = 10,000(2^0.03t), where t is the number of years from the present and P is the
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Question 1119052: The population of a town is 10,000 people. The population is growing according to the function P(t) = 10,000(2^0.03t), where t is the number of years from the present and P is the population. What is the estimated population of the town after 3 years.
I can set the problem up but have a difficult time inputting in my calculator TI-84 plus
P(t) =10,000 (2^.03t)
P (3) = 10^4 (2^,03(3)
P (3) 10^4 (2^.09) after inputting this should give me the answer.
Found 4 solutions by Theo, greenestamps, josgarithmetic, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i just so happen to have the TI-84 plus so you're in luck.
the function is p(t) = 10,000 * 2 ^ .03t.
that's a strange looking formula.
are you sure it isn't p(t) = 10,000 * e ^ .03t ?????
that would make more sense.
the letter e represents the scientific constant of 2.718281828...
that formula then gives you the continuous growth rate, which is what is usually used in these type of problems.
i'll do both, just in case you really meant 2.
first i'll use the 2.
10,000 * 2 ^ .03t, when t is equal to 3, is calculated as follows in the TI-84 Plus calculator.
you enter 10000*2^(.03*3) and the calculator tells you the answer is 10643.70182 after you hit ENTER.
your entry of 10^4(2^.09) ENTER results in the same answer.
now i'll use e.
10,000 * e ^ .03t, when t is equal to 3, is calculated as follows in the TI-84 Plus calculator.
you enter 10000*2ndLN.09) and the calculator tells you the answer is 10941.74284
2ndLN gets you e^( which you then fill in with .09).
try it out and see if you get the answer you are looking for.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
I'm not sure what you are asking here.
Are those three expressions EXACTLY what you input to your TI84 on different tries?
The first won't give you the right answer, because the calculator won't know what to do with the comma in "10,000". Further more, it will do the exponentiation before the multiplication; it will be evaluated as
instead of
The second expression you show is an invalid input....
The third expression you show gives the right answer; except that it of course has to be rounded to a whole number.
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
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town is 10,000 people. The population is growing according to the function P(t) = 10,000(2^0.03t), where t is the number of years from the present and P is the population. What is the estimated population of the town after 3 years.
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P is like THIS:
P(t)=10000*2^(0.03t)
Question means, what is P when t=3?
You had the steps, just written incorrectly.
10640=P
-
not sure what accuracy you want to keep;
Given population probably not exactly 10000 to the nearest 1 people
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
The population of a town is 10,000 people. The population is growing according to the function P(t) = 10,000(2^0.03t), where t is the number of years from the present and P is the population. What is the estimated population of the town after 3 years.
I can set the problem up but have a difficult time inputting in my calculator TI-84 plus
P(t) =10,000 (2^.03t)
P (3) = 10^4 (2^,03(3)
P (3) 10^4 (2^.09) after inputting this should give me the answer.
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