The number​ H(t) of veterans from foreign wars who are homeless or at risk of becoming homeless can be approximated by the exponential​ function, H(t)=55(1.65)t​,

Question

The number​ H(t) of veterans from foreign wars who are homeless or at risk of becoming homeless can be approximated by the exponential​ function, H(t)=55(1.65)t​, where t is the number of years since 1999.

​a) In what year were there 14,000 veterans who were homeless or at risk of becoming​ homeless?

​b) What is the doubling time of homelessness among​ veterans?

Answer 1

a) 1990 = base year. 2001 is 11 years later, when homelessness reaches 14,000

14000/55 = 254.54 = (1.65)^t, t = 11.06 years

b) doubling time is 2=(1.65)^t t = about 0.002 years = 0.024 months = 0.024(30) days = 0.72 days = 17.28 hours = 17 hours and 17 minutes is the doubling time. 55 in 1990. 110 17 hours later.

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