Answer
a.) 2.4
b.) 1.224
c.) 0.496
Work Step by Step
Given the formula: v(t)= (100t)/(2t+15), use the quotient rule to find the derivative, or a(t):
a(t)= [(2t+15)(100) - (100t)(2)] / [(2t+15)^{2}]
a(t)= [(200t+1500)- 200t]/ [( 4t^2 + 60t + 225)] OR
a(t) = 1500 / (4t^2 +60t+225)
Plug in each given time:
A.) a(5) = 1500/[4(5^2) +60(5) +225] --> 1500/(100+300+225)
--> 1500/625
a(5)= 2.4
B.) a(10)= 1500/[(4(10^2) +60(10) +225] --> 1500/(400+600+225)
--> 1500/1225
a(10)= 1.224
C.) a(20)= 1500/[4(20^2) +60(20) +225] --> 1500/(1600+1200+225) --> 1500/ 3025
a(20)= 0.496
