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Math - graphing

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i am having trouble with a graphing calculator please help with these two questions
1. a census was taken from 2012 to 2020. the data collected is given in the following table. 2012-2020
L1 l2
0 6000
1 6300
2 6615
3 7012
4 7362
5 7878
6 8429
7 9272
8 10199

a) what is the exponentail equation for the data (is it P=pe(rt)

B) Using your calculator determine the predidcted annual population to the nearest whole number in the year 2030.

2. A student fires a model rocket into the air. The rocket reaches a maximum height of 24.8 meters and lands 55 meters from the student. (assume parabola)
a) list thress points on the trajectory
b) determine the regression equation that best fits the trajectory using your graphing calculator.

I have spent the last two hours on this please help me walk through this as i really just want to know how to do this

  • Math - graphing -

    Yes, the general equation is P=pe^(rt), or P=p*k^t

    If that's the equation, then the terms form a geometric sequence, since each is k times the one before. Let's examine the ratios:

    6300/6000 = 1.05
    6615/6300 = 1.05

    Looks like P = 6000 * 1.05^t

    If ou want it in terms of e^x, then since 1.05 = e^(ln 1.05)

    P = 6000 * e^(ln 1.05 * t) = 6000*e^(.049t)

    where t is years since 2012

  • Math - graphing -

    so i came up with 14440 people rounded to the nearest whole number.
    is there a way to check the formula by using the previous information?

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