Test Last Chance Exam 4 The poplation ofery was 74 thousand m 1992 The exponenti

Question

Test Last Chance Exam 4 The poplation ofery was 74 thousand m 1992 The exponential powth tate was 15% per year 1111 a) Find the expenential growth function in terms of t where t is the samber of years since 1992. a) Find the )Predict the population in 2007, to the nearest thomand Round to the nearest thousand as terded) c) ln what year wil the population be 87 thousand? Roand to the nearest year as teeded.) 1Take a Test- + auzzes & Tests × x: https://www.mathol.com/Student/PlayerTest.aspxtestld- 1083128378 centerwin-y

Explanation / Answer

a) P(t) = 74000 e0.015t

b) Population in 2007, P(15) = 74000 e0.015*15 = 74000*1.25 = 97671.881

c) 87000 = 74000 e0.015t

87/74 = e0.015t

1.18 = e0.015t

log 1.18 = 0.015t

0.0702 = 0.015t

t = 0.0702/0.015

t = 5 years

In 1997 population will be 84000

2. a) P(t) = P ekt

P(t) = P e0.07t

b) P = 9000 at t = 5

P(t) = 9000 e0.07*5

= 12771.6

c) 18000 = 9000 e0.07t

2 = e0.07t

ln 2 = 0.07t

0.69 = 0.07 t

t = 0.7/0.07 = 10 years

3. P(t) = P e-0.00012t

23P/100 =P e-0.00012t

ln (23/100) = -0.00012t

-1.5 = -0.00012t

t = 1.5/0.00012 = 12500 years

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