The percentage of southern Australian grasshopper eggs that hatch as a function of temperature (for temperatures between 7°C and 25°C) can be modeled asg(t)0.0065t4 0.49t3 - 13t2136.3t - 394 percentwhere t is the temperature in °C, data from 7 sts 25.t(a) What temperature between 7°C and 25°C corresponds to the greatest percentage of eggs hatching? (Round your answer to three decimal places.)9.47x °CWhat is the percentage at this input? (Round your answer to three decimal places.)96.672%(b) What temperature between 7°C and 25°C corresponds to the least percentage of eggs hatching (Round your answer to three decimal places.)?25°CWhat is the percentage at this input? (Round your answer to three decimal places.)10.69

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Asked Nov 15, 2019
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The percentage of southern Australian grasshopper eggs that hatch as a function of temperature (for temperatures between 7°C and 25°C) can be modeled as
g(t)0.0065t4 0.49t3 - 13t2136.3t - 394 percent
where t is the temperature in °C, data from 7 sts 25.t
(a) What temperature between 7°C and 25°C corresponds to the greatest percentage of eggs hatching? (Round your answer to three decimal places.)
9.47
x °C
What is the percentage at this input? (Round your answer to three decimal places.)
96.672
%
(b) What temperature between 7°C and 25°C corresponds to the least percentage of eggs hatching (Round your answer to three decimal places.)?
25
°C
What is the percentage at this input? (Round your answer to three decimal places.)
10.69
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The percentage of southern Australian grasshopper eggs that hatch as a function of temperature (for temperatures between 7°C and 25°C) can be modeled as g(t)0.0065t4 0.49t3 - 13t2136.3t - 394 percent where t is the temperature in °C, data from 7 sts 25.t (a) What temperature between 7°C and 25°C corresponds to the greatest percentage of eggs hatching? (Round your answer to three decimal places.) 9.47 x °C What is the percentage at this input? (Round your answer to three decimal places.) 96.672 % (b) What temperature between 7°C and 25°C corresponds to the least percentage of eggs hatching (Round your answer to three decimal places.)? 25 °C What is the percentage at this input? (Round your answer to three decimal places.) 10.69

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Expert Answer

Step 1

Given, function is

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g(t)-0.0065t* + 0.49t -13t2 +136.3t -394 --(1)

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Step 2

For greatest and least temperature, differentiate equation (1) and find the critical points and checking the values at the critical points and end points.

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d 8(t)=(-0.0065ť + 0.49t -13t +136.3t -394) dt d = -0.0065 d 0.49()-13 ) 1363 (0) +136.3(1)- 0 (394) dt dt dt dt dt --0.0065(4r)+0.49(3r?) -13(2r) --0.026 1.47t - 26t +136.3 ...2)

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Step 3

Taking derivative is ...

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-0.026t31.47t2-26t+136.3 = 0 t =9.437Real root t 23.551 0.930i<Imaginary root t =23.551 -0.930i Imaginary root

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