# APPLICATIONS OF SOLVING EXPONENTIAL EQUATIONS USING LOGARITHMS

# 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?

Round your answer to the nearest hour.

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 = Pe^{rt} , 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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