Answer:
The exponential function to model the situation is p = 10800[tex](0.975)^{\textrm t}[/tex]
Step-by-step explanation:
Given as :
The population of small town in 2002 = 10,800
The rate of decrease in population = r = 2.5%
Let The number of years of population decrease = t years
Let The population after n years = p
Now, According to question
The population after n years = The population of small town in 2002 × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
or, p = 10800 × [tex](1-\dfrac{\textrm r}{100})^{\textrm t}[/tex]
or, p = 10800 × [tex](1-\dfrac{\textrm 2.5}{100})^{\textrm t}[/tex]
or, p = 10800 × [tex](0.975)^{\textrm t}[/tex]
∴ p = 10800[tex](0.975)^{\textrm t}[/tex]
Hence, The exponential function to model the situation is p = 10800[tex](0.975)^{\textrm t}[/tex] . Answer
