Question

Ashly's speed in mph at time t after getting onto Highway 5 is given by

v(t) = 0.011t5 -0.178t4 +0.473t³ + 1.672t² + 3.388t +29.485
for time t> 0 measured in minutes.
a. How fast was Ashly driving when she first got onto Highway 5?

Answer 1

Ashly was driving at 29.485 mph when she first got onto Highway 5, as determined by evaluating the constant term of her velocity function v(t) at t = 0 minutes.

Step-by-step explanation:

The student's question asks about the speed at which Ashly was driving when she first got onto Highway 5.

To find this, we need to evaluate the given velocity function v(t) at t = 0 minutes.

The velocity function provided is v(t) = 0.011t5 - 0.178t4 + 0.473t3 + 1.672t2 + 3.388t + 29.485, which represents Ashly's speed in mph at time t after getting onto the highway.

Upon substitution of t = 0 into the function, the terms containing t will all be zero, because any number to the power of zero is zero, and any number multiplied by zero is zero. This leaves us with the constant term:

v(0) = 29.485 mph

Therefore, Ashly was driving at 29.485 mph when she first got onto Highway 5.