Question

On the basis of data collection, a biologist found that the number of fruit flies, on any day, t, and with a limited food supply, could be approximated by the exponential model shown below:  
N(t)=360/1+39e^-0.12t   
t ≥ 0
Use your graphics calculator as needed to answer these questions but explain what you entered into the calculator.  
(a) What was the initial fruit fly population in the experiment?
(b) What is the rate of change in the fruit fly population between t = 10 and t = 20, rounded down to the nearest whole fruit fly?
(c) What is the rate of change in the fruit fly population if t =18, rounded down to the nearest whole fruit fly?
(d) What is the first value of t when there will there be at least 100 fruit flies?
(e) If time were unlimited, what is the maximum fruit fly population that could be expected under this lab experiment?
(f) What is the average fruit fly population over the first 10 days. rounded down to the nearest whole fruit fly?

Answer 1

Number of facet flies on one dayt and with a limited food supply INCH) = 360 1+ 3800127 where tro. o initial jeuét fly populatou e put of=o of NCHI NAI celetso - 360 = 360 = 9 1+29 4p (6) Route of change inferuit fly population - Poetween of=10 and f = 20 INCHI = 360 (1 +39 0 0 0 12 4 - 2 34X=8:12 ot FONCH) = 360739 x 0.12 x 80.12f/ Tot 71+39 0-0 12 4 1 2 ONCHI = 3.1232 It of = 10

ONfH at at +=20 7.4218 parte of change in fewest fly population Betuleyst=iu dud H=23 Jante Deo 67 )tzen = 7:4218 – 3.1232 = 4.298 a 4 (whole Number) (C) porte of change in the fault fly population 19 = 18 Bonn = 6.428 _ 3 H:18 - (d) N(A) = 100 when find out t 160 = 360 143980.124 t = 124.99938 + 125 I 125

@ il time wear unlimeted ( t o ) svax puinem fecert.dly population N(E) : 360

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