Please help me solve this word problem

Question

In 1997, lowe's had 427 stores nationwide. By 1999, this total had grown to 520. If the number of stores continues to grown exponentially at this rate, how many stores will there be in 2017? 

Answer 1

 

Exponential growth Function is given by

 

P(t)= P₀ .e ^kt

 

In this equation P₀ represents the stores at initial (in 1997)= 427

 

P(t)= size at time t (in 1999)=520

 

t= 1999-1997=2

 

k=Exponential growth rate

 

substituting all values

 

520 = 427 e^2k

 

divide both side by 427

 

1.2178 = e^2k

 

Take ln of both side

 

ln 1.2178 = 2k

 

0.1970 = 2k

 

0.0985 = k

 

Now

 

the number of stores continues to grown exponentially at this rate, how many stores will there be in 2017

 

t= 2017-1997=20

 

P(t)= P₀ .e ^kt

 

P(20)= 427. e^(0.0985)20

 

        =427.e^1.9704

 

        =427. 2.7182^{1.9704                         (value of e=2.7182)}

      

        =3063.03

       

        = 3063

 

So number of store in 2017 is 3063