11 15 points A population of zombies is growing quickly Init

11. [15 points] A population of zombies is growing quickly. Initially, there were 125 zombies. Six days later. there were 515 zombies. (a) If the growth is exponential, write an equation Z(t) for the number of zombies t days after the initial outbreak. (b) Evaluate and interpret Z(14). Round your answer to the nearest whole mumber. Be sure to write your interpretation in a complete sentence (c) If the trend continues, when will there be 2,000 zombies? Round your answer to the nearest day after the beginning of the outbreak. Be sure to write your interpretation in a complete sentence.

Solution

initial population is 125 zombies

6 days later = 515

so we can write the function as

515 = 125 e^ k(6)

k = 0.235975

hence , equation becomes

Z(t) = 125 e^ 0.235975 t

where t is days after initial breakout

b) Z(14) = 125 e^ 0.235975 (14)

Z(14) = 2216

c) 2000 = 125 e^ 0.235975 t

2000/ 125 = e^ 0.235975 t  

t = 12

so after 12 days the zombie population will be 2000