Given:
The initial population = 750,000
23% of the population becomes a zombie everyday.
To find:
The function that represents p, the number of unaffected people after x days.
Solution:
The general exponential decay function is:
[tex]P=P_0(1-r)^x[/tex] ...(i)
Where, [tex]P_0[/tex] is the initial population, r is the rate of decay and x is the time period.
We know that,
The initial number of unaffected people = 750,000
The unaffected people decreasing by 23% . The decimal form of 23% is 0.23.
Putting [tex]P_0=750000, r=0.23[/tex] in (i), we get
[tex]P=750,000(1-0.23)^x[/tex]
[tex]P=750,000(0.77)^x[/tex]
Therefore, the required function is [tex]P=750,000(0.77)^x[/tex], where p is the number of unaffected people after x days.
