Pre-Calc Unit 3

Exponentials

100

Which are exponential functions?

3^x      x⁵      -2⁴      x^x

3^x

200

Solve without a calculator

5³=5^x

x=3

300

2^x=16

x=4

400

(1/2)^x=1/8

x=3

500

Solve without a calculator

e^x=5

x=ln(5)

Logarithmic

100

Solve without a calculator

log₂(8)=y

y=3

200

Solve without a calculator

log₄x=2

x=16

300

Solve without a calculator

log(x)=3

x=10³ = 1000

400

Solve without a calculator

log_b(36)=2

b=6

500

Solve without a calculator

log_x+4(64)=2

x=4

Ln

100

Solve without a calculator

ln(e³)=y

y=3

200

Simplify using log/ln rules

ln(x⁴)

4ln(x)

300

Simplify using log/ln rules

ln(x/5)

ln(x)-ln(5)

400

Put into condensed form

2ln(x)-4ln(2)

ln(x^2/2^4)

500

Simplify 

ln(e^2/2)

ln(e^2)-ln(2)

2ln(e)-ln(2)

2-ln(2)

Logistic

100

Where do you find the limit to growth in a logistic function?

The value in the numerator

200

What is the limit to growth in the function

P(t)= (12,790)/(1+2,402e^(-0.0309x))

12,790

300

Based on the New york population model (population is in millions)

P(t)=(19.875)/(1+57.993e^(-0.035005t))

What will New York's population be after 215 years?

19,272,737

400

Based on the New york population model (population is in millions)

P(t)=(19.875)/(1+57.993e^(-0.035005t))

What is New York's Maximum sustainable population (limit to growth)?

19,875,000

500

Based on the New york population model (population is in millions)

P(t)=(19.875)/(1+57.993e^(-0.035005t))

"What will the population be after 50 years?"

1,794,558

Compounding interest

100

What is the n value for compounding:

Monthly?

Yearly?

Quarterly?

Monthly=12

Yearly=1

Quarterly=4

200

Set up the equation to measure the amount of money in an account over time if you invest $5000 compounded monthly at a 7% interest rate

A=5000(1+.07/12)^(12t)

300

Find the amount of money accumulated if you invest $1500 at a 7% interest rate for 6 years compounded annually.

$2251.10

400

Compound interest Yearly for 5 years on $10,000 at 20% interest. Suppose I deposit this money into an interest bearing account in 2012 and want to know how much it will be worth at the end of 2017. How much would it be worth?

$24,883

500

If someone invests $15,000 into an account with a 8% interest rate compounded monthly, how long will it be until the account contains $45,000?

13.78 years