Until women reach their mid60s they tend to get less sleep p

Until women reach their mid-60s, they tend to get less sleep per night as they age. The average number of hours (in excess of eight hours) that a woman sleeps per night can be modeled as s(w) = 2.697(0.957^w) hours when the woman is w years of age, 15 lesser than or equal to w lesser than or equal to 64.up arrow How much sleep, in excess of eight hours, do women of the following ages get: 15, 22, 45, 64? (Round your answers to three decimal places.) Using the results from part (a), write the function for the model giving age in years, where s + 8 hours is the average sleep time, with data from the values of s found in part (Round all numerical values to three decimal places.)

Solution

s+8 = 2.697(0.957)^w

(s+8)/2.697 = 0957^w

Taking log of both sides:

log{( s+8)/2.697} = 0.957 logw

1/0.957 { log{( s+8)/2.697} } = logw

log{( s+8)/2.697}^1.044 = logw

Equating the argumant inside the log :w = ( s+8)/2.697}^1.044