Question

in 1990, 28% of bicycles in a certain country had tires wider than 25mm. throughout the 1990s, this increased by approximately 0.6% per year. if this trend continues, in which year will 76% of bicycles in the country have tires wider than 25mm?
in \boxed{ }, 76% of bicycles in the country will have tires wider than 25mm.

Explanation:

Step1: Define variables and formula

Let $y$ = number of years after 1990, $P(y) = 28 + 0.6y$ (linear growth model, since it's a constant annual percentage point increase)

Step2: Set up equation for 76%

$28 + 0.6y = 76$

Step3: Solve for y

Subtract 28 from both sides:
$0.6y = 76 - 28 = 48$
Divide by 0.6:
$y = \frac{48}{0.6} = 80$

Step4: Calculate target year

Add y to 1990:
$1990 + 80 = 2070$

Answer:

2070