Choose all that are best modeled by an exponential function. A town with an initial population of 2,000 doubling in size every 10 years. A car rental that cost $20 a day plus $0.05 per mile. A bank account with a starting balance of $1,000 compounded annually at 5%. A sugar processing plant producing 2 tons of sugar per month.

Exponential functions for the following example will be given as follows:
a] A town with an initial population of 2,000 doubling in size every 10 years.
solution:
The exponential function for this example will be:
f(t)=ab^(nt)
where:
a=initial size
b=growth rate
t=time
n=number of terms
thus plugging in our values we obtain:
f(t)=2000(2)^t/10


b]A car rental that cost $20 a day plus $0.05 per mile. 
This example will follow a linear equation of the form y=ax+b, where a=rate, 
b=constant amount.
From our example:
a=$0.05 per mile
b=20 dollars per day
x=number of miles
Thus the function will be:
f(x)=0.05x+20

c] A bank account with a starting balance of $1,000 compounded annually at 5%.
Here we shall use the compound interest formula to obtain our value:
FV=P(1+r/100)^t
where:
FV=future value
P=principle amount
r=rate
t=time
thus, plugging in our value in the equation we obtain:
P=$1000; r=5%, time=t

f(t)=1000(1+5/100)^t
f(t)=1000(1.05)^t
Hence the function representing the case is:
f(t)=1000(1.05)^t

d] A sugar processing plant producing 2 tons of sugar per month.
This will be modeled using linear function, such that the total will be given by:
f(x)=2x
where:
x is the number of months:
thus the cases that are best modeled by exponential function is:
A and C