Exponential Functions Review

Geometric Sequences

100

Write the explicit formula and find a₁₁ for -4, 2, -1, 1/2, . . . 

Write your answer as a fraction. 

a_n=-4(-1/2)^n-1

a₁₁= -1/256

200

Find the 15th term of the geometric sequence 3,−6,12,...

49152

300

The first five terms of a sequence are a₁=625, a₂=500, a₃=400, a₄=320, and a₅=256. Write an explicit formula to find a_n. Use the formula to find a₉.

a_n= 625(0.8)^n-1

a₉= 104.8576 or 65536/625

400

Write an explicit formula for the graph above. 

a_n=(-7)(1/2)^n-1

500

Write an explicit formula for the graph shown below. Find a_0. What does a₀ represent?

a_n= 6(3/4)^n-1

a₀= 8 

a₀ is the y-intercept

Exponential Growth/Decay

100

6900 dollars is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 26 years, to the nearest cent?

$54,196.92

200

A new car is purchased for 17300 dollars. The value of the car depreciates at 9.25% per year. What will the value of the car be, to the nearest cent, after 15 years?

$4034.09

300

Bentley invested $26,000 in an account paying an interest rate of 6.8% compounded daily. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 11 years?

$54928.20

400

Dylan invested $7,200 in an account paying an interest rate of 2.3% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 12 years?

$9481

500

Ella invested $4,800 in an account paying an interest rate of 2.125% compounded quarterly. Santiago invested $4,800 in an account paying an interest rate of 2.375% compounded daily. After 18 years, how much more money would Santiago have in his account than Ella, to the nearest dollar?

$331

Write y=ab^x

100

Write the exponential function represented by the table: 

y = 5(3)^x

200

Write the exponential function that includes the points (0, 0.2) and (1, 0.6)

y = 0.2(3)^x

300

Write the exponential function for the graph: 

y = -5(3/5)^x

400

Write an exponential function for the graph: 

y = 4(3/2)^x

500

Write an exponential function in the form y=ab^x that goes through the points (0,15)and (2,735). 

y = 15(7)^x

Graphing Exponential Functions

100

Describe the transformation from the solid to the dotted line: 

Reflect over the y-axis, translate down 1 unit

200

Describe the transformations from the solid to the dotted line: 

Translated left 3 units and up 5 units

300

Write the exponential function that is graphed: 

y = (1/4)^x-4 

400

Describe the transformations from the solid to the dotted line. Then write the function. 

Reflect over the x-axis, translate 4 units right 

y = -2^x-4

500

Graph: f(x)=3(1/3)^x+1

Write Exponential Functions with Transformations

100

If f(x)=2^x write the equation of a function g(x) which would shift the graph of f(x) left 2 units.

g(x) = 2^x+2

200

If f(x)=−2^x write the equation of a function g(x) which would shift the graph of f(x) right 2 units and down 1 unit.

g(x) = -2^x-2-1

300

If f(x) = 2^x write a function g(x) which reflects f(x) over the x-axis, shifts right 3 units, and vertically stretches by a factor of 4. 

g(x) = -4(2)^x-3

400

Given f(x) = 3^x, write the function g(x) which is shown below: 

g(x) = 3^x+4-1

500

Given f(x)=  2^x, write the function g(x) which is shown below: 

g(x) = -3(1/2)^x-8