The population of Hat clue Coon Arkansas can be modeled by t

The population of Hat clue Coon, Arkansas can be modeled by the function: P(t) = 19e^rt where t is time in years after 2009. In 2013, the population had grown to 29. Find the EXACT value of r and rounded to 5-decimal places. At this rate how long will it take for the population to double? Round your answer to the nearest 10th of a year Draw the angle in standard position: theta = pi/12 = 105degree Convert the angle to radian measure as a multiple of pi (not as a decimal): degree = 130degree Convert from turns to degrees: theta = 17pi/12 = 255degree

Solution

P(t) = 19 e^rt

t = time in years in 2009

in 2013 population is 29

therefore , from 2009 to 2013 that is 4 years population is 29

so we can write

29 = 19 e^ 4r

dividing both sides by 19

29/19 = e^4r

1.5263 = e^4r

taking ln on both sides

ln 1.5263 = 4r ln e ( ln e = 1)

.42285 = 4r

dividing both sides by 4

.10570 = r

r = .10570

b) lets say population doubles in t years

P(t) = 19e^rt

when population will double P(t) becomes 19*2 = 38

38 = 19 e^.10570 t

dividing both sides by 19

38/19 = e^.10570 t

2 = e^.10570 t

taking ln on both sides

ln 2 = .10570t ln e (ln e =1 )

t = 6.56 years approximately population will double