Final answer:
The yearly growth factor for a decade growth factor of 2.5 is approximately 1.10, which corresponds to an annual growth rate of about 9.65% when expressed as a percentage.
Step-by-step explanation:
To find the yearly growth factor when given a decade growth factor of 2.5, we can use the formula for compound interest which is also applicable for growth rates: F = P(1 + r)^n, where F is the future value after n years, P is the principal amount (initial value), and r is the annual growth rate.
In this case, we have a decade growth factor of 2.5, so the future value after 10 years, F, would be 2.5 times the initial value, P. We want to find the yearly growth factor, which means we need to solve for (1 + r) in the equation 2.5 = (1 + r)^10.
To do this, we take the 10th root of 2.5:
(1 + r) = ∐2.5^(1/10)
Using a calculator, we can find that 1 + r is approximately 1.0965. Therefore, the yearly growth factor is about 1.10 when rounded to two decimal places.
The annual growth rate can be calculated by subtracting 1 from the growth factor: 0.0965, or 9.65% when expressed as a percentage.