Algebra 2 Unit 4 Review

Log base 10 Values

100

solve

y=log₁₀10,000

4

200

Solve

y=log₁₀1,000,000

6

300

Solve

y=log₁₀ 1X10²⁵

25

400

What 2 integers will the solution lie between

y=log₁₀425,000

5 and 6

500

What integer must the solution be greater than

y=log₁₀ 3,125,654

6

Natural Logarithms and e

100

What is the logarithmic form of e^x=y?

ln y=x

200

What is the exponential form of ln y = x

e^{x = y}

300

How would you find the solution to ln (23) on the graph of y= e^x

Find the point on the curve at y=23 and find the corresponding x-coordinate

400

How would you use the graph of e^x = y to find e⁴?

Find the point on the curve where x=4 and estimate the y-coordinate

500

Solve

y= ln (2.718281828)

1

Solving exponential equations

100

Solve

8*10^x = 800,000

x=5

200

Solve and write the solution in exact form

4*10^3x = 48,000

y=(log 12,000)/3

300

Solve and write in exact form

7 * 3^x = 7/27

x=-3

400

Solve

18*5^x = 450

x=2

500

Solve 

250 e^.5x =13,000

x=(ln 52)/.5

Graphs of Exponential and Logarithmic Functions

100

Would the point (16,2) lie on the graph of 

y= log₄ x and why?

4²=16 so yes

200

What would the x-intercept of the graph of 

y= log₁₆ x be and why?

1 because 16⁰=1 and the x-intercept is where y=0

300

In a graph representing 2 exponential growth functions, what does the intersection represent?

Where both functions have the same x and y values.

400

In a graph representing 2 exponential functions, how do you determine which has a larger initial value?

The curve with a higher y-intercept

500

In a graph representing 2 exponential functions how do you determine which has a larger growth rate?

It is the graph that is increasing faster

Misc. Unit 4 Questions

100

Solve for d in exact form

1000=250e^.036d

(ln 4)/.036

200

Solve for x in exact form

256= 16e^.05x

x=(ln 16)/.05

300

The area of an invasive plant on a lake in square feet is given by f(x)=15(3^x) where x represents days since it was measured. When will this plant cover 1215 square feet?

4 days later

400

The expression: 10e^.0062t models the balance in thousands where t represents time in years since the account was opened. What does the .0062 represent?

The interest rate

500

The expression: 10e^.0062t models the balance in thousands where t represents time in years since the account was opened. Write an expression to represent the year, t, there will be 250,000 in the account.

(ln 25)/.0062