Question

By our standards, Xenia-Lepton aliens are huge, strange creatures and their reproductive method is fascinating: while under the influence of a massive gravitational field, a mature Xenia-Lepton sheds several billion sub-atomic particles. These particles combine to form a seed which, if viable, grows rapidly by direct conversion of dark energy to matter. The rate of growth is directly proportional to how much the juvenile has yet to grow before reaching the height of a Xenia-Lepton adult. All adult Xenia-Leptons have exactly the same height, which is 98m. The coefficient of proportionality for the growth rate has been determined to be 0.046 . 1) Determine the height of a Xenia-Lepton alien that is 42 years old. 2) When a Xenia-Lepton reaches exactly 99.0% of the adult height, they change colour from bright, shining gold to pitch black. At what age does this occur? Provide both answers with TWO decimal places, using the normal convention. Pad with zeros if necessary. Height at 42 years (m) = Age at colour-change (years) =

Answer 1