Multiple Choice 1 Suppose the value of your newly bought car

(Multiple Choice) 1) Suppose the value of your newly bought car, purchased at $15,000, loses 17% of its value every year. In this way, about how many years will it take for the value of the car to drop to $10,000? Construct a simple exponential decay model and use it to answer the question. Show work.

a) 1-1.5 years b) 1.5-2 years c) 2-2.5 years d) 2.5-3 years

(Multiple Choice) 2.) Find f^-1(x) and its range when f(x) = 3 - log₅(1 - x) Show work please!

a)  f^-1(x) = 1 + 125  · 5^x

b)  f^-1(x) = 1 - 125  · 5^x

c)  f^-1(x) = 1 + 125  · 5^-x

d)  f^-1(x) = 1 - 125  · 5^-x

3) Solve log₂x + log₂(x - 3) = 2

4) Show your work in detail. US Department of Wildlife tagged 100 black tailed rabbits in a national forest in 2009. In 2010 they tagged 120 black tailed rabbits in the same range. If the rabbit population follows the unibhibited exponential growth model, how many rabbits will be in the range 5 years from 2009?

5)(Show work) The half-life of Stronium is 30 years. If 50 grams is present now, how much will be present in 50 years? (Round your answer to three decimal places)

Solution

1. We have to use the following formula

A=A₀(1-r)^t

Here A=1000, A₀=15000, t=17%=.17

10000=15000(1-.17)^t

2/3= .83^t

Taking log on both sides

log(2/3)= t log.83

t= log(2/3)/log.83=2.18 years

That is in between 2-2.5 yrs

Correct option is c