Final answer:
To find the 'consonant' 'a' in the population growth equation P=5000eat for the city that had its population double from 5000 to 10000 in 10 years (from 1980 to 1990), we use the equation to solve for 'a', yielding approximately a = 0.0693.
Step-by-step explanation:
The question involves finding the value of the consonant 'a' in the exponential growth formula P = 5000eat given that the population of the city was 10000 in 1990 (10 years after 1980). Since t = 0 corresponds to 1980, for t = 10 (1990), we can insert the population value P = 10000 into the equation to solve for 'a'.
By substituting P = 10000 and t = 10 into the equation, we get:
- 10000 = 5000e10a
- e10a = 2
- 10a = ln(2)
- a = ln(2) / 10
After calculating, the value of 'a' is found to be:
a = 0.0693, approximately.