Question

A rare coin appreciates at a rate of 5.2% a year. If the initial value of the coin is $500, after how many years will its

Answer 1

Answer: 36 years

Step-by-step explanation:

Exponential equation to represent growth:-

$y=A(1+r)^t$ , where A is the initial value , r is the rate of growth and t is the time period.

Given : A rare coin appreciates at a rate of 5.2% a year. If the initial value of the coin is $500.

i.e. Put A= 500 and r= 0.052 in the above formula.

The amount after t years:

$y=500(1.052)^t$

Inequality for value cross $3,000 mark:

$3000$

Divide both sides by 500

$6$

Taking log on both sides , we get

$\log6\dfrac{0.778151250384}{0.0220157398177}=35.345223773\\\\t\approx36$

Hence, it will take approx 36 years to cross the $3,000 mark.