Question

A point moves along a straight path. The function f ( t ) = log 2 ( t ) determines the distance (in meters) the point has traveled in terms of the number of seconds t since the point started moving. How far has the point traveled 21 seconds after it started moving? meters If the point has traveled 3.16993 meters, how many seconds have elapsed since it started moving? seconds 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 − 1 ( d ) =

Answer 1

Answer:

a) 4.392317 mt

b) 9 seconds

c) $\large f^{-1}(d)=2^d\;sec.$

Step-by-step explanation:

We have

$\large f(t)=log_2(t)$

where t is given in seconds and t in meters.

a)How far has the point traveled 21 seconds after it started moving?

By replacing t=21 in our equation we get

$\large f(21)=log_2(21)=4.392317 \;mt$

b)If the point has traveled 3.16993 meters, how many seconds have elapsed since it started moving?

We need to find a t such that f(t) =3.16993.  

This can be accomplished by using the definition of $log_2$

$\large f(t)=3.16993\rightarrow log_2(t)=3.16993\rightarrow t=2^{3.16993}=9\;sec.$

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.

$f^{-1}$ is given by the definition of log

$\large f^{-1}(d)=2^d\;sec.$