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Using the given values from the table, we can create two equations:
P(2) = a(b)^2 = 12,100
P(3) = a(b)^3 = 13,310
Dividing the second equation by the first equation gives:
P(3)/P(2) = (a(b)^3)/(a(b)^2) = (a(b)^3)(1/a(b)^2) = b
Therefore, we can conclude that b = P(3)/P(2) = 13,310/12,100.
Substituting this value of b into the first equation:
12,100 = a(b)^2 = a(13,310/12,100)^2
Simplifying:
12,100 = a(1.100)^2 = a(1.21)
Therefore, a = 12,100/1.21 = 10,000.
So the expression for P(t) is:
P(t) = 10,000(13,310/12,100)^t