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1. Gregory may choose between two accounts in which to invest \$5000. Account A offers 2.3% annual interest compounded monthly. Account B offers       continuous compound interest. Greg plans to leave his investment untouched (no further deposits and no withdrawals) for 10 years.

Which account will yield the greater balance at the end of 10 years?

How much more money does Greg earn by choosing this more profitable account

2. Given log_5 3=0.6826 and log_5 8=1.2920, evaluate the expressions.

(a) log_5 2

(b) log_5 (75/8)

3.  A hive of bees contains 27 bees when it is first discovered. After 3 days, there are 36 bees. It is determined that the population of bees increases exponentially.

How many bees are will there be after 30 days? Express your answer as an exact value and rounded to the nearest whole number.

Nov 28, 2019

#1
+109563
+1

1.

Compounded monthly =   5000 ( 1 + .023/12)^(10*12)  = \$6291.61

Continuous compounding  =  5000e^(.023* 10)  =  \$6293

Nov 28, 2019
#2
+109563
+1

2 (a)

log 5 2  =    log 5  8^(1/3) =   (1/3) log5 8  =  (1/3) (1.2920)  ≈  .430667

Nov 28, 2019
#3
+109563
+1

2. (b)

log5 (75/8)  =  log5 [ ( 5^2 * 3) /  8 ]   =   log5 5^2  + log5 3  -  log 5 8  =

2 log5 5   + log5 3  - log5 8 =

2 (1)   + 0.6826  - 1.2920   =

2  + 0.6826  - 1.2920  =

1.3906

Nov 29, 2019