Patty has paid $10 per hour. Tyler gets paid $1 for the first hour $2 for the second hour $4 for the third hour and so on when will tyler get pais more per hour than patty
Tyler's rate is exponential, or it can be said if forms a geometric sequence, having the form:
f=ir^(t-1), f=final value, i=initial value, r=common ratio or "rate", t=time
We can see that the common ratio is 2 because 2/1=4/2=2 is constant. Each term is twice the previous term. And we also know that the initial value is $1 so:
f=1(2^(t-1)) or just
T=2^(t-1)
We want to know when T>P so
2^(t-1)>10 taking the natural log of both sides
(t-1)ln2>ln10 dividing both sides by ln2
t-1>ln10/ln2 add 1 to both sides
t>(ln10/ln2)+1
t>4.32 (to the nearest hundredth of an hour)
Since I guess that we should assume that the rates only change after incremental or integer values for t.
Tyler will earn more per hour than Patty starting in the 5th hour.
