Word Problem

Question

A factory kept increasing its output by same percentage every year. Find the percentage if it is known that output is doubled in the last two years.

Answer 1

This is an exponential growth:

 

      Output = (Output₀)*(1 + r)t

 

Where:

• OUTPUT is the output of the factory = 2*OUTPUT₀ at t=2
• OUTPUT₀ is the initial factory output at t = 0
• r is the growth rate expressed as a decimal = unknown
• t = years = 2

 

Let's plug in the values and solve for the unknown, r:

      Output = (OUTPUT₀₎*(1 + r)^t

      2*OUTPUT₀ = (OUTPUT₀)*(1 + r)²

      2 = (1+r)²

      √2 = 1+r

      √2 - 1 = r

      1.4142 - 1 = r

      0.4142 = r

 

To express as a percent, multiply by 100%

 

      0.4142*100% = r

      41.42% = r