SOLUTION: A point moves along a straight path. The function f(t)=log2(t) determines the distance (in meters) the point has traveled in terms of the number of seconds t since the point star

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Question 1124889: A point moves along a straight path. The function f(t)=log2(t) determines the distance (in meters) the point has traveled in terms of the number of seconds
t since the point started moving.
a. How far has the point traveled 18 seconds after it started moving?
b. If the point has traveled 2.80735 meters, how many seconds have elapsed since it started moving?
c. Write a function f^-1 that determines the number of seconds that have elapsed since the particle started moving in terms of the distance (in meters) the particle has traveled, d.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The function f%28t%29=log%282%2Ct%29 determines the distance (in meters) the point has traveled in terms of the number of seconds t since the point started moving.
a. How far has the point traveled 18+seconds after it started moving?
f%28t%29=log%282%2Ct%29 when t=18+ seconds
f%2818%29=log%282%2C18%29
f%2818%29=log%2818%29%2Flog%282%29
f%2818%29=log%282%2A3%5E2%29%2Flog%282%29
f%2818%29=log%282%29%2Flog%282%29%2B2log%283%29%2Flog%282%29
f%2818%29=1%2B2log%283%29%2Flog%282%29
f%2818%29=1%2B3.169925
f%2818%29=4.169925 meters

b.
If the point has traveled 2.80735 meters, how many seconds have elapsed since it started moving?
f%28t%29=log%282%2Ct%29 when f%28t%29=2.80735+
2.80735=log%282%2Ct%29
2.80735=log%28t%29%2Flog%282%29
2.80735log%282%29=log%28t%29
log%282%5E2.80735%29=log%28t%29
t=2%5E2.80735
t=6.99998

c.
Write a function f^-1 that determines the number of seconds that have elapsed since the particle started moving in terms of the distance (in meters) the particle has traveled, d.
f%5E-1 is inverse, and inverse of log is exponential:
recall: d=log+%282%2Cy%29=>y=2%5Ed
f%5E-1%28d%29=2%5Ed