Writing and interpreting exponential functions

The amount of cola in a soda machine decreases by a rate of 5% each hour. The amount of cola in the machine was originally 75 gallons.

Which function models the amount of cola in gallons after h hours?

• f(h) = 75(-5)^h

• f(h) = -5(75)^h

• f(h) = .95(75)^h

• f(h) = 75(.95)^h

The cost of tuition at a local university is $12,000. The tuition is increasing at a rate of 6% per year. Write an exponential function to model this situation if x is the time in years.

• C(t) = 12000(.94)^t

• C(t) = 12000(1.94)^t

• C(t) = 12000(.06)^t

• C(t) = 12000(1.06)^t

A population of ants increases by a factor of 5 each year. Initially there were 450 aunts. Which equation represents the amount of aunts after 9 years?

Let y represent the total amount of aunts after x years.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

What is the equation for this problem?

​ y=​​ (a)   (​ (b)   )^​ (c)  

• $78,200.00
• 1.04
• 10
• .96

Lin's account has an initial balance of $150 and it doubles every month. Which equation represents the growth of Lin's account?

• y = 150 + 2^x

• y = 150 ⋅ 2x

• y = 150 + 2x

• y = 150 ⋅ 2^x

An antibiotic is introduced into a colony of 12,000 bacteria during a laboratory experiment. The colony is decreasing by 14.9% per minute. Which function can be used to model the number of bacteria in the colony after x minutes?

• f(x) = 12000(1 + 14.9)^x
• f(x) = 12000(1 - 14.9)^x
• f(x) = 12000(1 + 0.149)^x
• f(x) = 12000(1 - 0.149)^x

What is the explicit rule for the sequence:
11, 22, 44, 88...

• _gn = 2(11)^n-1
• _gn = 11x2
• _gn = 11(2)^n-1
• g_n = 11+(2)^n-1

Write an equation for this problem: Mrs. Madison brings in 3 dozen donuts for your class. Each hour, y'all eat a third of them. How many donuts would be left after x hours?

•  $y=3\left(\frac{1}{3}\right)^x$  

•  $y=3\left(\frac{2}{3}\right)^x$  

•  $y=36\left(\frac{2}{3}\right)^x$  

•  $y=36\left(\frac{1}{3}\right)^x$