The heptathlon is an Olympic competition - Leaving Cert Mathematics - Question (b) - 2016

For part (iii), we need to find the value of $c$ given:
$1087 = a(b - x)^c$
Where:

• $a = 0.11193$
• $b = 254$
• $x = 2$ minutes and 1.84 seconds = 121.84 seconds.
• This gives us: $1087 = 0.11193(254 - 121.84)^c$
  Calculating the subtraction:
  $254 - 121.84 = 132.16$
  So we substitute back into:
  $1087 = 0.11193(132.16)^c$
  Dividing both sides by $0.11193$:
  $\rac{1087}{0.11193} = (132.16)^c \ \\ 9711.4268 = (132.16)^c$
  Applying logarithms:
  $log_{10}(9711.4268) = c imes log_{10}(132.16)$
  Calculating:
  $log_{10}(9711.4268) \ \\ \\approx 3.987$ and $log_{10}(132.16) \ \\ \ \\approx 2.121$
  Thus, we solve for $c$:
  c = \ rac{3.987}{2.121} \ \\ \ \ ext{ which approximates to } 1.88.