Exponential Functions

43 -1 2 13

Solve each exponential equation.1

(a) 2 32 (b) x x xx

e ee

3 -1 52 2x

3 1 5x

2x

42 1 7

3

xx x

x

ee e

e

2 1 7x x 1

9x

A credit union pays interest of 4% per annum compounded quarterly on a certain savings plan. If $2000 is deposited in such a plan and the interest is left to accumulate, how much is in the account after 1 year?

1Interest after first quarter: 2000 0.04 $20

4I

New Principal =2000 20 $2020

1Interest after second quarter: 2020 0.04 $20.20

4I

New Principal =2020 20.20 $2040.20

1Interest after third quarter: 2040.20 0.04 $20.40

4I

New Principal =2040.20 20.40 $2060.60

1Interest after fourth quarter: 2060.60 0.04 $20.61

4I

New Principal =2060.60 20.61 $2081.21

Find the amount A that results from investing a principal P of $2000 at an annual rate r of 8% compounded continuously for a time t of 1 year.

0.08 12000eA 0.08 1 $22000 16 5e 6. 7

Suppose you want to open a money market account. You visit three banks to determine their money market rates. Bank A offers you 4% annual interest compounded daily, Bank B offers you 4.1% compounded monthly, and Bank C offers 3.95% compounded continuously. Determine which bank is offering the best deal.

Bank A Bank B Bank C

3650.04

1 1365er

0.0400808er

4.008%er

120.041

1 112er

0.0417793er

4.178%er

0.395 1er e

0.0402905er

4.029%er

Bank B is offering the best deal

What annual rate of interest compounded quarterly should you seek if you want to double your investment in 6 years?

4 6

2 14

rP P

24 2 1

4

r

244 2 1r 0.1171089

The annual rate of interest needed to double the principal in 6 years is 11.71%

24

2 14

r

(a) How long will it take for an investment to double in value if it earns 6% compounded continuously?

(b) How long will it take to triple at this rate?

0.06(a) 2 tP Pe0.062 te

0.06ln 2 ln teln 2 0.06t

ln 211.55 years

0.06t

0.06(b) 3 tP Pe0.063 te

0.06ln 3 ln teln 3 0.06t

ln 318.31 years

0.06t