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25r = ln(1.875) ≈ 0.6292 → r ≈ 0.6292 / 25 = 0.025168.
Annual growth rate = 0.025168 × 100 ≈ <<0.025168*100=2.5168>>2.52%.
#### 2.52
A bioinformatician compares two bacterial genomes: Genome A has 4,200 genes, and 18% are metabolic genes. Genome B has 30% more metabolic genes than A. How many metabolic genes are in Genome B?
Metabolic genes in A = 18% of 4,200 = 0.18 × 4,200 = <<0.18*4200=756>>756.
Genome B has 30% more: 756 × 1.3 = <<756*1.3=982.8>>982.8 → rounded to nearest whole number = 983.
#### 983
An astronomer tracks a comet that orbits a star every 192 years. If the comet’s semi-major axis is 20 AU, and Kepler’s third law states T² = a³ (in AU and years), what is the calculated orbital period and how does it compare to the observed data?
Using law: T² = a³ → T² = 20³ = 8,000 → T = √8,000 ≈ <<sqrt(8000)=89.44>>89.44 years.
Observed period is 192 years, so the model underestimates T² by factor of 8,000 / 89.44² = 8,000 / 8,000 ≈ 1 — perfect match.
