Explanation:
A
f(x) = 72 × 1.25 × x
so, the price is $90 after 1 year (72×1.25×1).
$180 after 2 years (72×1.25×2)
$270 after 3 years (72×1.25×3)
and so on.
or did you mean
f(x) = 72 × (1.25)^x
so, still, the price is $90 after 1 year (72×1.25^1).
$112.50 after 2 years (72×1.25^2).
$140.625 = $140.63 after 3 years (72×1.25^3)
that makes more sense. I will continue with that assumption.
so, the price is increasing, as every factor of the multiplication is positive and larger than 1. therefore, it only goes up.
and due to the formula, the price of every year is the price of the previous year multiplied by 1.25.
a multiplication by 1.25 is an increase of 25% (compared to a constant multiplication by 1).
so, the price increases every year by 25%.
B
year 1
price $65
year 2
price $84.50 difference $19.50
100% = 65
1% = 65/100 = 0.65
19.5/0.65 = 30% difference
year 3
price $109.85 difference $25.35
100% = 84.5
1% = 84.5/100 = 0.845
25.35/0.845 = 30% difference
year 4
price $142.81 difference $32.96
100% = 109.85
1% = 109.85/100 = 1.0985
32.96/1.0985 = 30% difference
so, product B has the greater percentage increase in the price (30% vs. 25%).