There's no such concept as "close" in mathematics. Or at least, you have to specify when you consider two numbers to be "close".
All we can say is that, since 3/4=0.75, the two numbers are

units apart. Is this small enough to consider them as "close"? Is this big enough to consider them not to be "close"?
You should clarify more what you mean so that a definitive answer can be given.
we are given
A collector’s item is purchased for $150
so,

its value increases by 3% each year
so,

t is time in years
Let's assume cost of item after t years is C(t)
so, we can use formula

now, we can plug values


so, equation is

After doubling
C(t)=2*150=300
so, we can set C(t)=300
and then we can solve for t

we get

so, doubling time is 23.44977 years.........Answer
Graph:
we can draw graph of

Answer:

Step-by-step explanation:
This is the answer I got when I solved it