Question

The population of a city is growing according to the exponential model p = cekt, where p is the population in thousands and t is measured in years. if the population doubles every 11 years what is k, the city's growth rate? [round answer to the nearest hundredth.]
a.2.8%
b.4.4%
c.6.3%
d.8.9%

Answer 1

Answer: C. 6.3%

Step-by-step explanation:

Answer 2

P = ce^(kt)
make p = 2c because doubling will be
like c-->2c, so if p = 2c, then
p = ce^(kt)
2c = ce^(kt)
2c/c = (ce^(kt))/c
2 = e^(kt)
Now take natural logarithm (ln) of both sides of the equation:
ln (2) = ln (e^(kt))
0.693 = kt×ln e
**this is because ln of an exponent makes the exponent become multiplied by the ln,
and ln e = 1
0.693 = kt×ln e
0.693 = kt×1, and t = 11 years
0.693 = k(11)
0.693/11 = 11k/11
k = 0.063, multiply by 100 to get %
k = 6.3%
answer is C