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This printable supports Common Core Mathematics Standard HSF-LE.A.2

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# Constructing Exponential Functions (Grades 11-12)

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## Constructing Exponential Functions

1.
What is the equation of the exponential function graphed below? Assume that the scale of both axes is one unit.
1. $f(x) = 2^x$
2. $f(x) = 10^x$
3. $f(x) = e^x$
4. Not enough information
2.
What is the equation of the exponential function in the following graph? Assume that the scale of both axes is one unit.
1. $f(x) = 2^x$
2. $f(x) = 2^x + 3$
3. $f(x) = 5^x$
4. $f(x) = 10^x - 5$
3.
The following table gives some of the values of $f(x)$. Using these values, what is the function rule for this exponential function?

 $\ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \$ $\ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \$ $0$ $5$ $1$ $10$ $2$ $20$ $3$ $40$
1. $f(x) = 2*5^x$
2. $f(x) = 5*e^x$
3. $f(x) = 2^x + 5$
4. $f(x) = 5*2^x$
4.
Create an exponential function of the form $f(x) = ab^x,$ given the points $(-2,5)$ and $(3,10)$. The numerical values of $a$ and $b$ have been rounded in the following answers.
1. $f(x) = 6.61*1.15^x$
2. $f(x) = 0.10*0.14^x$
3. $f(x) = 7.94*1.26^x$
4. At least three points are needed.
5.
Given the points $(1,2)$ and $(8,9)$, which of the following exponential functions could be created with them? The numerical values in the function have been rounded.
1. $f(x) = 1.41*1.42^x$
2. $f(x) = 1.61*1.24^x$
3. $f(x) = 2.74*1.16^x$
4. All of the above.
6.
There are 20 rabbits living on an island, and the population triples every year. Which of the following functions correctly models this situation, where $P$ is the population of rabbits, and $t$ is the number of years since the current population count?
1. $P(t) = 20 + 3^t$
2. $P(t) = 20t^3$
3. $P(t) = 3t + 2$
4. $P(t) = 20*3^t$
7.
There is a 100 g sample of Sodium-24 sitting in a secure storage box. After 15 hours, there is only 50 g left. Which function best describes this relationship between the amount of Sodium-24, $S$, and the time that has elapsed, in hours, $t$?
1. $S(t) = 100*(1/2)^(15t)$
2. $S(t) = 100 e^(-0.046t)$
3. $S(t) = 50*(1/2)^(15t)$
4. $S(t) = 50 e^(-0.5t)$
8.
A lab keeps blood samples in a special fridge, which is kept at 0 °C, for a certain experiment. After the blood is initially taken from a patient and put in the fridge, its temperature is checked every 30 minutes for the first two hours. Below are those recordings. Which exponential function rule best describes this information?

 $\ \ \ \ \ \ \ \ \ \ \ mathbf{"Time in Fridge (min)"} \ \ \ \ \ \ \ \ \ \ \$ $\ \ \ \ \ \ \ \ \ \ \mathbf{"Temperature (°C)"} \ \ \ \ \ \ \ \ \ \$ $30$ $19.2$ $60$ $10.5$ $90$ $5.8$ $120$ $3.2$
1. $f(t) = 35.2 * (-0.02)^t$
2. $f(t) = 35.2 * 0.98^t$
3. $f(t) = 6.8 * 1.08^t$
4. There is not enough information given in the table to find the function rule.
9.
A store relies on word of mouth advertising so it brings in 30 potential customers and gives them \$100 gift cards if they will each tell 5 friends within a week. If each of those people tell 5 more friends within a week and the pattern continues, how many people will hear about the store after 10 weeks?
1. 488,281,250
2. 624,431,250
3. 292,968,750
4. 128,281,250
10.
A bacteria colony covers $5 \ "cm"^2$ and grows exponentially. After 4 days it covers $80 \ "cm"^2$. How much area will it cover after 2 weeks?
1. $8.2 \ "m"^2$
2. $4300 \ "cm"^2$
3. $4.3 \ "m"^2$
4. $1393 \ "cm"^2$
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