we are given
A collector’s item is purchased for $150
so,
[tex]P=150[/tex]
its value increases by 3% each year
so,
[tex] r=0.03 [/tex]
t is time in years
Let's assume cost of item after t years is C(t)
so, we can use formula
[tex]C(t)=P(1+r)^{t}[/tex]
now, we can plug values
[tex]C(t)=150(1+0.03)^{t}[/tex]
[tex]C(t)=150(1.03)^{t}[/tex]
so, equation is
[tex]C(t)=150(1.03)^{t}[/tex]
After doubling
C(t)=2*150=300
so, we can set C(t)=300
and then we can solve for t
[tex]300=150(1.03)^{t}[/tex]
we get
[tex]t=23.44977 [/tex]
so, doubling time is 23.44977 years.........Answer
Graph:
we can draw graph of
[tex]C(t)=150(1.03)^{t}[/tex]
