The number of employees working for Cogsworth Cogs in 1996 was 24,405 24,405 , with an expected decrease of 3.5% 3.5 % per year. At the percent of decrease gi

Question

help I don't how to do it 

Answer 1

Jules, you have an exponential growth or decrease problem.

For each year after 1996 the number of employees decreases by

3.5% so for each year the number of employees is 96.5% of the

previous year.  Your equation for number of employees as a

function of time is:

 

e(t) = 24405(0.965)^t  where t is number of years after 1996

 

Example:  How many years will pass before Cogsworth has 20000 employees?

 

20000 = 24405(0.965)^t

20000/24405 = 0.965^t

log(20000/24405) = log 0.965^t

log(20000/24405) = t(log 0.965)

 

t = [log(20000/24405)]/(log 0.965) = 5.6 years

 

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Example 2:  How many employees will Cogsworth have in the year 2000?

 

For this problem t=4 since 2000 is 4 years after 1996

 

e(t) = 24405(0.965)⁴ = 21163.5  rounded:  21,164 employees