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%
Accepted Solution
A:
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