Question

In 1928, when the high jump was first introduced as a women's sport at the Olympic Games, the winning jump

for women was 70.0 inches, while the winning jump for men was 86.5 inches. Since then, the winning jump for
women has increased by about 0.48% per year, while the winning jump for men has increased at a slower rate,
0.4%. If these rates continue, when will the winning jump for women be higher than the winning jump for men?
after 110 years
after 248 years
after 265 years
after 270 years

Answer 1

D) After 270 years

Answer 2

Explanation:

Given that in 1928, f(x) = the winning jump

for women was 70.0 inches and g(x) = the winning jump for men was 86.5 inches.

Increase = 0.48% for women and 0.4% for men

i.e. after x years
`f(x) =70(1.0048)^x \\\\g(x) = 86.5(1.004)^x`

Let us find when these two values would be equal.

That is at point of intersection

Solving we get x =244 years

Hence approximately after 248 years women will exceed men.