Final answer:
The frequency of cats with long tails and short tails, as well as the frequency of homozygous dominant cats and the frequencies of the T and t alleles in the gene pool, can be determined using the formulas derived from the Hardy-Weinberg equilibrium.
Step-by-step explanation:
To determine the frequencies of the different genotypes, we can use the formulas derived from the Hardy-Weinberg equilibrium.
a. The frequency of cats with long tails (TT and Tt genotypes) can be calculated as p² + 2pq, where p represents the frequency of the T allele. As given, the population is in Hardy-Weinberg equilibrium, so we can assume that p² + 2pq + q² = 1. Since q represents the frequency of the t allele, the frequency of cats with long tails can be found using the formula p² + 2pq = 1 - q².
b. Similarly, the frequency of cats with short tails (tt genotype) can be found using the formula q².
c. The frequency of cats that are homozygous dominant (TT genotype) is equal to p².
d. The frequency of the T allele in the gene pool of this population is equal to p.
e. The frequency of the t allele in the gene pool of this population is equal to q.