U1T2

Exponential Functions

100

Solve 17⁶+19²

24137930

200

Chad invests $12,000 at a 5% annual interest rate, compounded annually. Write a function A(t) that finds the amount Chad has in his account after t years. Explain what the y-intercept represents. Describe the end behavior of the graph of A(t) as t increases.

A(t) = 12,000(1.05)t; y-intercept is the amount that Chad started with, $12,000; as t → ∞, A(t) → ∞.

300

Write and solve an equation to determine the balance after 25 years in an account that had an initial investment of $18,000 at 3% interest, compounded annually.

18000(1+0.03)^(25)=37688.00

400

The average savings account interest rate for 2012 was 0.06% compounded quarterly. Suppose you invest $42,001 in either investment for t years. Write an equation that models the growth of the savings account.

A(t)=42001(1+.0006)^t

500

What is the general form for a function that models exponential growth based on an interest rate compounded annually?

A(t)=P(1+r)^t

Continuous compounding and the number e

100

Solve for x: e^3x=4

x=0.462098

200

What is e¹ to the 3rd decimal place?

2.718

300

What is x for 9^x-3=.01

x=.904097

400

A new car is purchased for $32,000. It depreciates continuously at a rate of 13%. What is an exponential function that represents the value of the car after t years?

A(t)=-32000e^-.13t

500

What is does the below function approach/converge to when n goes to ∞?

(1+1/n)ⁿ

e

Logarithms

100

Evaluate log₄262

Approx. 4.016711

200

Expand log(7/8)

log7-log8

300

What is the most reduced form of:

[log(x)-log(3x+1)]+log(10000)

log(x/(3x+1))+4 (some variations)

400

What is the change of base formula?

log_ax=(log_bx)/(log_ba)

500

Explain why ln(1)=0

Because of the definition that states log_b(x)=a if and only if x=b^a

1=e⁰

Common and natural log

100

Solve ln(e)

1

200

What is x when log(3x)=0

1

300

Use the properties of logs to expand:

ln(x/yz)

ln(x)-(ln(y)+ln(z))

400

Evaluate 856=ln(e^2x)

428

500

log(x-5)+logx=log(2x)

 

Using properties and change of base formula

100

2 ln 3x = 12

x=e⁶/3=134.476

200

4(2^2x-1) + 5 = 29.

x=1.792

300

Solve ln (2x − 3) + ln (x + 2) = 2 ln x for x.

x=-3 and x=2

400

log (x + 5) = log (x − 1) − log (x + 1)

No solution

500

Jose invested $100,000 in a retirement account that averages 6.5% interest compounded continuously. How long will it take for him to double his money?

200000=100000e^(0.065t)

t=10.664