Question

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 1

Answer:

(a)4.17 metres

(b)6.9999 seconds

(c)f⁻¹, t= 2ᶠ⁽ᵗ⁾

Step-by-step explanation:

f(t)=log₂t

(a) If t=18 seconds

f(18)=log₂18= log ₂(2X9)

=log ₂2 + log ₂9

=1+(log9/log2)

=1 + 3.1699 =4.17 metres

f(18)=4.17 metres.

(b)If f(t)=2.80735, we want to determine the value of t.

f(t)=log₂t

2.80735=log₂t

Changing from logarithm form to index form

t= 2^(2.80735)

=6.9999 seconds

(c)f(t)=log₂t

Next, We want to determine f⁻¹

If y=log₂t

Changing to exponential form

t=2ʸ

f⁻¹, t= 2ᶠ⁽ᵗ⁾.