Question

When a snake hatched 4 years ago, it was only 5 inches long. Suppose it is now 3 foot 9 inches long. Given that the annual percentage rate has been constant, what is the annual percentage rate of growth for the snake? A) 58.28% B) 63.33% C) 73.21% D) 78.94%

Answer 1

The most important thing here is converting the length into the same units. So:

3 feet 9 inches = 45 inches

now, we know that compound 'growth' can be worked out by multiplying the initial value by the decimal to the power of the years. So, relating to this question, the equation would be:

5 x α⁴ = 45

Now, we have to solve for α!

α⁴ = 45/5
α⁴ = 9
α = ⁴√9
α = 1.732050808

This is the increase every year written as a decimal so, if we want to work out the pure percentage, we have to subtract 1 and then multiply by 100:

1.732050808 - 1 = 0.732050808
0.732050808 x 100 = 73.20508076

Rounded to 2 decimal places the answer would be 73.21% !