 # APPLICATIONS OF SOLVING EXPONENTIAL EQUATIONS USING LOGARITHMS

1) Depreciation (the decline in cash value ) on a car can be determined by the
formula V = C(1− r)t , where:

V = the value of the car after t years
C = the original cost
r = the rate of depreciation

If the car's cost, when new, is \$15,000, the rate of depreciation is 30%, and the
value of the car now is \$3,000, how old is the car to the nearest tenth of a year?

2) Growth of a certain strain of bacteria is modeled by the equation G = A(2.7)0.584t
where:

G = final number of bacteria
A = initial number of bacteria
t = time (in hours)

In approximately how many hours will 4 bacteria first increase to 2,500 bacteria?

3) The amount A, in milligrams, of a 10-milligram dose of a drug remaining in the
body after t hours is given the formula A =10(0.8)t . Find, to the nearest tenth of
an hour, how long it takes for half of the drug dose to be left in the body.

4) Sean invests \$10,000 at an annual rate of 5% compounded continuously ,
according to the formula A = Pert , where:

 A = amount r = rate of interest P = principal t = time (in years) e = 2.718

a) Determine, to the nearest dollar, the amount of money he will have after 2 years.
b) Determine how many years, to the nearest year, it will take for his initial
investment to double.

5) The equation for radioactive decay is where:

p = the part of the substance
H = half-life of substance
t = period of time that the substance remains radioactive

A given substance has a half-life of 6,000 years. After t years, one-fifth of the
original sample remains radioactive. Find t, to the nearest thousand years.

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