Math  /  Calculus

QuestionPart 1 of 3 HW Score: 61.11%,1161.11 \%, 11 of 18 points Points: 0 of 1
The growth rate of a fungus vari L(t)=2.4t+0.75cos(2πt24)L(t)=2.4 t+0.75 \cos \left(\frac{2 \pi t}{24}\right) (a) Calculate the growth rate dLdt\frac{\mathrm{dL}}{\mathrm{dt}}. (b) What is the largest growth rate of the microbe? What is the smallest growth rate? (a) Calculate the growth rate. dLdt=\frac{\mathrm{dL}}{\mathrm{dt}}=\square
Type an exact answer using π\pi as needed.)

Studdy Solution
Combine the results from STEP_1 and STEP_2 to find dLdt\frac{\mathrm{dL}}{\mathrm{dt}}:
dLdt=2.4π16sin(2πt24) \frac{\mathrm{dL}}{\mathrm{dt}} = 2.4 - \frac{\pi}{16} \sin\left(\frac{2\pi t}{24}\right)
The growth rate dLdt\frac{\mathrm{dL}}{\mathrm{dt}} is:
dLdt=2.4π16sin(2πt24) \frac{\mathrm{dL}}{\mathrm{dt}} = 2.4 - \frac{\pi}{16} \sin\left(\frac{2\pi t}{24}\right)

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