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.
Accepted Solution
A:
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