The question is an illustration of geometric progression.
The monthly cost of food in x years is [tex]\mathbf{y = 300 (1.04)^x}[/tex]
From the complete question, we have:
[tex]\mathbf{Food =\$300}[/tex] ---- the average amount spent on food, each month
[tex]\mathbf{Inflation =4\%}[/tex] --- the yearly inflation
So, the monthly amount (y) that will be spent on food in year (x) is:
[tex]\mathbf{y = Food \times (1 + Inflation)^x}[/tex]
Substitute known values
[tex]\mathbf{y = 300 \times (1 + 4\%)^x}[/tex]
Express percentage as decimal
[tex]\mathbf{y = 300 \times (1 + 0.04)^x}[/tex]
[tex]\mathbf{y = 300 \times (1.04)^x}[/tex]
Rewrite as:
[tex]\mathbf{y = 300 (1.04)^x}[/tex]
Hence, the monthly cost of food is:
[tex]\mathbf{y = 300 (1.04)^x}[/tex]
Read more about geometric progressions at:
https://brainly.com/question/14320920
