In a certain town, sociologists have determined that crime rates are influenced
ID: 2867390 • Letter: I
Question
In a certain town, sociologists have determined that crime rates are influenced by temperature by the equation C = 0.1(T - 60)^2 + 100 where C is the crimes per month and T is the temperature (in Fahrenheit). If the average temperature for May was 70 degree and was changing at 8 degrees per month, determine the rate of change of crimes per month. (8 points) For the function f(x) = e^5x , calculate the 12th derivative. (calculate and simplify the first few derivatives, then look for a pattern to predict the 12th derivative.Explanation / Answer
Question 9) 16 Answer
C= 0.1(T-60)^2 +100
dC/dt = 0.2 (T-60)dT/dt
dC/dt = 0.2 (70-60) * 8 [Given : dT/dt =8]
dC/dt = 16 crimes/month Answer
Question 10) 5^12e^5x Answer
f(x) = e^5x
f ' (x) = 5e^5x
f "(x) = 5^2e^5x
f '''(x) = 5^3e^5x
Similarly ,
12th derivative = 5^12e^5x Answer