1) Your friend purchases a new car, which costs them $36000. For every year after it is purchased, the car loses 17% of its value due to depreciation. What is the value of the car after 64 months?

2. A certain type of bacteria, given a favourable growth medium, doubles in population every 6 hours. 

a) After two days, there were 4096 bacteria. How many were there, initially?

b) How long would it take for there to be 65 536 bacteria?

 

ANSWER:

1. = $ 13326.59
2. a. = 16 bacteria.

           b. = 3 days

Step-by-step explanation

1. The value of the car after 64 months is given using the equation as follows:

A = P * (1-r)^t

where P is initial amount = $ 36000, r is rate of decrease = 0.17, t is time in years = 16/3 years (64 months)

therefore, A is given by:

A = 36000 * (1-0.17)^16/3

= $ 13326.59

2. a. The initial amount of the bacteria is given using the doubling equation given as:

A = P * (2)^t/6

where A is final amount = 4096, t is time in hours = 48 hours (2 days)

therefore, P is given by:

4096 = P * (2)^48/6

P = 4096/2⁸

= 16 bacteria.

b. The time taken for there to be 65 536 bacteria is given by:

A = 16 (2)^t/6

65536 = 16 (2)^t/6

therefore, t is given by

65536 = 16 (2)^t/6

(2)^t/6 = 4096

t/6 log 2 = log 4096

t = 6 log 4096/log 2

= 72 hours

= 3 days