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?

year 2194

Explanation:

1) Model the jump of the women:

i) initial jump = 70.0 in

ii) increase rate = 0.48% per year

iii) equation: h = 70.0(1 +0.0048)ⁿ

2) Model the jump of the men:

i) initial jump 86.5 inches.

ii) increase rate, 0.4%.

iii) equation: h = 86.5 (1 + 0.004)ⁿ

3) Equal the two equations (h = h) to find when the jumps will be equal:

i) 70.0(1 +0.0048)ⁿ = 86.5 (1 + 0.004)ⁿ

ii) 70.0(1.0048)ⁿ = 86.5 (1.004)ⁿ

ii) [1.0048ⁿ / 1.004ⁿ] = 86.5/70.0

iii) [1.0048/ 1.0040]ⁿ = 86.5/70.0

iv) n log (1.0048 / 1.0040) = log ( 86.5/70)

v) n = log (86.5/70) / log (1.0048/1.0040) ≈ 266

3) year = 1928 + 266 = 2194

That is in the year 2194

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