5/3 Exponential Functions

Given the exponential function $f\left(x\right)\ =200\left(\frac{1}{2}\right)^x$  , what is the "b" value and what does it represent?

• 200, the initial value

• 200, the constant ratio

•  $\frac{1}{2}$  , the initial value

•  $\frac{1}{2}$  , the constant ratio

Given the exponential function $f\left(x\right)\ =\ 1500\left(1.04\right)^x$ , what is the  "a" value and what does it represent?

• 1.04, the initial value

• 1.04, the constant ratio

• 1500, the initial value

• 1500, the constant ratio

• x = 2

• y = 4

• x = -2

• y = 3

• all real numbers

• y > 0

• x > 0

• x > 3

An antibiotic is introduced into a colony of 15,000 bacteria during a laboratory experiment. 72% of the bacteria decay every minute. Write a function that can be used to model the number of bacteria in the colony after m minutes.

• $f\left(m\right)=\ 15,000\left(0.72\right)^m$

• $f\left(m\right)=\ 15,000\left(1.28\right)^m$

• $f\left(m\right)=\ 15,000\left(0.28\right)^m$

• $f\left(m\right)=\ 15,000\left(1.72\right)^m$

The foundation of your house has about 1,800 termites. The termites grow at a rate of about 2.2% per day. Which exponential function could be used to represent the growth rate of the termites?

• $f\left(x\right)=\ 1800\left(2.2\right)^x$

• $f\left(x\right)=\ 1800\left(1.22\right)^x$

• $f\left(x\right)=\ 1800\left(0.022\right)^x$

• $f\left(x\right)=\ 1800\left(1.022\right)^x$

Given the equation $f\left(x\right)\ =\ 180\left(0.98\right)^x$  which represents the cooling temperature of a pot of coffee over time in minutes, when will the pot of coffee be approximately  $100\degree F$  ? Use the best approximated time.

• 30 minutes

• 45 minutes

• 50 minutes

• 60 minutes

Graph the given the exponential function $f\left(x\right)\ =100\left(\frac{5}{4}\right)^x$  , what is the "b" value and what does it represent?

•  $\frac{5}{4}$  , the rate of change

•  $\frac{5}{4}$  , the constant ratio of decay

•  $\frac{5}{4}$  , the initial value

•  $\frac{5}{4}$  , the constant ratio of growth

Which of the following graphs represents exponential growth?