On planet Zorba, a solar blast has melted the ice caps on its equator. 8 years…
2025
On planet Zorba, a solar blast has melted the ice caps on its equator. 8 years after the ice melts, tiny plantoids called echina start growing on the rocks. Echina grows in the form of a circle, and the relationship between the diameter of this circle and the age of echina is given by the formula d = 4·√(t − 8) for t ≥ 8, where d represents the diameter in mm and t the number of years since the solar blast. Jagan recorded the radius of some echina at a particular spot as 8 mm. How many years back did the solar blast occur?
- A.
8
- B.
12
- C.
16
- D.
24
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Correct answer: D
Concept: when a quantity is described by a square-root growth law of the form d = k·√(t − a), you recover the time t by isolating the square root, then squaring to undo it. Before substituting, make sure the value you put in matches the variable in the formula — here the formula uses the diameter, while the data gives the radius, and diameter = 2 × radius.
Given: radius = 8 mm, so diameter d = 2 × 8 = 16 mm. Growth law: d = 4·√(t − 8) for t ≥ 8.
Substitute d = 16 into the formula: 16 = 4·√(t − 8).
Isolate the square root by dividing both sides by 4: 4 = √(t − 8).
Square both sides to remove the radical: 16 = t − 8.
Solve for t: t = 16 + 8 = 24.
Cross-check: put t = 24 back into the formula — 4·√(24 − 8) = 4·√16 = 4 × 4 = 16 mm = diameter, matching the 8 mm radius. The value t = 24 also satisfies the domain t ≥ 8.
Result: the solar blast occurred 24 years ago.