Problem of the Week - Algebra and Up - March 21, 2021 to March 27, 2021

Algebra and Up: 

Question: Sebastian wins a 0.5 inch long goldfish at a county fair. Every year, the goldfish's length increases by 25%. The goldfish lives for 21 more years. Write an equation for the length of the fish x in terms of the number of years t that have passed since the county fair. 

Answer: x = 0.5(1.25)^t

Solution:  Every year, the length of the goldfish is multiplied by 1.25. Since the additional length compounds, we’re going to need to multiply by 1.25 a number of times equal to the number of years since the fair. So we’re going to raise our 1.25 to the power of t. This gives us x = 0.5(1.25)^t.