Answer:
Option (3).(Bottom left)
Step-by-step explanation:
Formula for the exponential growth is,
h(x) = [tex]a(1+\frac{r}{100} )^{t}[/tex]
where r = rate of exponential growth
a = initial amount
t = duration or time
Option (1) (Top left)
h(t) = [tex](1+0.18)^{\frac{t}{6}}[/tex]
= [tex](1+\frac{18}{100})^t[/tex]
Rate of exponential growth will be,
r = 18%
Option (2) (Top right)
k(t) = [tex](\frac{3}{8})^t[/tex]
= [tex](1-\frac{5}{8})^t[/tex]
= [tex](1-0.625)^t[/tex]
= [tex](1-\frac{62.5}{100})^t[/tex]
r = -62.5%
This function shows the exponential decay rate of 62.5%.
Option (3) (Bottom left)
f(t) = [tex]1.36^t[/tex]
= [tex](1+0.36)^t[/tex]
= [tex](1+\frac{36}{100})^t[/tex]
r = 36%
Option (4) (Bottom right)
g(t) = [tex]0.86^t[/tex]
= [tex](1-0.14)^t[/tex]
= [tex](1-\frac{14}{100})^t[/tex]
r = -14%
This function shows the decay rate of 14%.
Therefore, Option (3). (Bottom left) shows the greatest exponential growth.
