# 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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Step 1

Given, function is

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.

Step 3

Taking derivative is ...

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