Question

your favorite math teacher bought an 1895 abacus that Albert Einstein received for his 16th birthday for $1,000. each year it appreciates in value by 5%. Which equation can be used to find the value, v, of the abacus x years after it was purchased?

Answer 1

Answer:

$v=1000(1+0.05)^x$

Explanation:

If the abacus appreciated by 5%, we can say that the value after one year will be:

v1 = 1000(1 + 0.05)

So, after 2 and 3 years the value will be:

v2 = v1 ( 1+ 0.05)

v2 = 1000(1 + 0.05)(1 + 0.05)

v2 = 1000(1 + 0.05)²

v3 = v2 ( 1+ 0.05)

v3 = 1000(1 + 0.05)²(1 + 0.05)

v3 = 1000(1 + 0.05)³

Therefore, after x years, the value v of the abacus will be:

$v=1000(1+0.05)^x$