Module 8 Review

Exponential Functions

100

In the function g(x) = 4^x, what is the base?

4

200

In the function f(x) =2^x, what is the domain?

All real numbers

300

In the function f9x) = 2^x, what is the range?

All numbers greater than 0 or y > 0.

400

In the function g(x) = 4^x, what is the y-intercept?

(0, 1)

500

Describe the end behavior of the function g(x) = 4^x.

As x approaches positive infinity, g(x) approaches positive infinity.

As x approaches negative infinity, g(x) approaches 0.  

Transformations

100

In the function f(x) = 3(2)^x + 7, what is the base?

2

200

In the function f(x) = 3(2)^x + 7, the +7 part represents what type of transformation?

Translation up 7 units

300

In the function f(x) = 3(2)^x + 7, the 3 represents what type of transformation?

Vertical stretch by a factor of 3

400

Consider the function f(x) = 3(2)^x + 7. If this function were translated down 2 units, how would this function change?

The +7 would become +5

500

Consider the function f(x) = 3(2)^x + 7. If this function were translated right 4 units, how would this function change?

The exponent would become (x - 4)

Natural Base e

100

The natural number e is equal to approximately...

2.718...

200

In the function f(x) = e^x, what is the asymptote?

y = 0

300

Describe the end behavior of the function f(x) = e^x

As x approaches positive infinity, g(x) approaches positive infinity.

As x approaches negative infinity, g(x) approaches 0.  

400

Consider the function f(x) = 2e^x - 3. If this function were reflected across the x-axis, how would it change?

The 2 would become negative. 

500

In the function f(x) = e^x, which x-coordinate is associated with the f(x) = 20.086?

x = 3

Compound Interest

100

In the compound interest formula, 

A = 800(1 + .03/12)¹²⁽⁴⁾, what is the principle?

$800

200

In the compound interest formula, 

A = 800(1 + .03/12)¹²⁽⁴⁾, what is the interest rate?

3%

300

In the compound interest formula, 

A = 800(1 + .03/12)¹²⁽⁴⁾, how often is the interest compounding per year?

Monthly

400

In the formula, A = 475e^0.045(7), how many years is the account accruing interest?

7 years

500

In the formula, A = 475e^0.045(7), how often is the interest compounding per year?

Continuously

Graphing to Find t

100

When using the graphing method on you calculator to determine the value of an exponent (such as time), how many functions are you graphing?

2 functions

200

When using the graphing method on you calculator to determine the value of an exponent (such as time), you have to graph both the exponential function given and what other type of function?

A horizontal line

300

A fossil has 13% of its Carbon-14 left. The formula to date a fossil is N(t)=100e^-0.00012t. How old is the fossil rounded to the nearest thousand years?

17,000 years old

400

Use a graphing calculator to find the number of years it takes for an investment to grow to $2000 (rounded to the nearest tenth of a year) if the initial investment is $1700 and earns 4.8% per year. 

3.5 years

500

The initial amount of a radioactive isotope given to a patient for medical imaging is 175mg. The time it takes for the isotope to decay can be modeled by the function A(t) = A_oe^-012t. After how many hours (rounded to the nearest whole hour, will there be less than 45 grams of the isotope remaining?

Approximately 12 hours