Suppose there were 2 043 Math 141 students 2011 In 2012 ther

Suppose there were 2, 043 Math 141 students 2011. In 2012 there were 1, 986 Math 141 students enrolled. Find the percent change in students from 2011 to 2012. Round to the nearest hundredth of a percent. Write an exponential function that models the number of Math 141 students since 2011. Call this function a(t). According to a (t), if the trend continues, how many Math 141 students will there be in 2016? Show your work and round to the nearest whole number. According to the graph of a (t), in which year will the number of Math 141 students reach 1500? Explain how you obtained your answer.

Solution

Row 1 : P(t) = 39(1.27)^t

Intial value = 39 ; Growth as factor >1 ; So, Growth factor : 1+r = 1.27 ; r = 0.27 ; In % = 27.5 %

Row 2 : P(t) = 5(0.08)^t ; Decay as factor < 1 ; So,Decay factor : 1-r = 0.08 ; r = 0.0.92 ; In % = 92%

Row 3 : Given Intial value :1200 ; factor = 1.10 ; Its a Growth ; Growth factor : 1+r = 1.10 ; r = 0.10 ; In % = 10%

P(t) = 1200(1.10)^t

Row 4 : Given Intial value :82 ; factor = 0.75 ; Its a Decay ; Decay factor : 1- r = 0.75 ; r = 0.25 ; In % = 25%

P(t) = 82(0.75)^t

Row 5 : Intial value = 542 lbs ; Decay ; Rate = 32% ; Decay factor = 1- 0.32 = 0.68

P(t) = 542(0.68)^t

Row 6 : Intial value = 89 ; Growth ; Rate = 85% ; Growth factor = 1.85

P(t) = 89(1.85)^t