There is a wellstudied panda population in Wuyipeng In 1986

There is a well-studied panda population in Wuyipeng. In 1986 there were 27 pandas and the researchers determined that they had an annual population growth of 1.053.

Which exponential model represents this population?
A. (1.053)27x
B. (27)1.053x
C. 27(1.053)x
D. (1.053)x

Use your model to predict how many pandas there will be in 2001.
(Express your answer rounded up to the nearest panda.)

_____________

Solution

Given dX / dt = 1.053 X (option D is correct )

using variable seperable method

dX / X = 1.053 dt integrating either side

log X =   1.053 t +log C   

removing log on eitherside

X = C e^{1.053 t} put t=0 ( whic represents the year 1986) we get 27 = C

X = 27 e^{1.053 t}

WHEN WE WISH TO PREDICT THE POPULATION IN 2001 Ie t=15 (2001-1986)

X₂₀₀₁= 27 e^{1.053 x15}

= 27 e ^15.795

= 27 (