Introduction to Exponential Functions

Poll

Let's see what we know about exponential functions already! Click on all options that you think represent an exponential relationship

• $$f\left(x\right)=2^x$$  

• $$f\left(x\right)=x^2-16$$  

• $$f\left(x\right)=\left(\frac{1}{2}\right)^x$$  

• $$f\left(x\right)=x^3$$  

Poll

Can you determine which graph below represents exponential DECAY?

• I really have no clue, I've never heard of an exponential

• $$f\left(x\right)=x^3$$  

​Write this down:

​Given that f(x)= ab^x, why does it make sense that a cannot = 0? What kind of function would you have if a = 0?

​

​

​Given that f(x)= ab^x, why does it make sense that b cannot = 1? What kind of function would you have if b=1?

Multiple Choice

What type of function is 

$$y=7\left(5\right)^x$$  ?

• Exponential Growth

• Exponential Decay

• Linear

• None of the above

Multiple Choice

What is the y-intercept of this function 

$$f\left(x\right)=2\left(\frac{1}{7}\right)^x$$  ?

• (0, 1/7)

• (0, 7)

• (0, 2)

• (2, 1/7)

Multiple Choice

What type of function is  

$$f\left(x\right)=2\left(1\right)^x$$  ?

• Exponential Growth

• Exponential Decay

• None of the Above

​Can you find the rate of exponential growth/decay?

Multiple Choice

Find the growth rate "r" (as a percentage) given the function: $$f\left(x\right)=3\left(1.02\right)^x$$  

• 1.02%

• 2%

• .02%

• 200%

Multiple Choice

The function shows the growth of a fruit fly population. f(t) is the number of fruit flies after t days.

What is the initial population of the fruit flies?

• $$100$$

• $$1.05$$

• $$105$$

• $$95$$

Multiple Choice

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

• y = 15(35)^x

• y = 15(1.35)^x

• y = 15(0.35)^x

• y = 35(1.15)^x

Multiple Choice

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y=5000(0.7)^x

• y=30(5000)^x

• y=5000(1.3)^x

• y=5000x^x

Multiple Choice

Hannah deposits $3000 in a savings account that pays interest at an annual rate of 4%. If no other money is added or withdrawn from the account, how much will be in his account after 10 years?

• $3122.18

• $4994.50

• $4440.73

• $86,776.40

Multiple Choice

JP buys a new computer for $2100. The computer's worth decreases by 50% annually. How much is it worth after 2 years?

• 225

• 325

• 425

• 525

Poll

In general, this is how I feel about what we learned today:

• I do not understand it AT ALL

• Ehh...I feel "exponentially" better than I did 50 minutes ago, but still not 100%

• I feel really good!