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Homework answers / question archive / If the number of telephone solicitations increases exponentially (continuously), how long will it take to double your number of annoying phone calls if the rate of growth is 12% per day?   

If the number of telephone solicitations increases exponentially (continuously), how long will it take to double your number of annoying phone calls if the rate of growth is 12% per day?   

Math

If the number of telephone solicitations increases exponentially (continuously), how long will it take to double your number of annoying phone calls if the rate of growth is 12% per day? 

 

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5.7762 days

Step-by-step explanation

The general formula of continuous exponential growth and decay is:

y = aekt

where:

y = final amount

a = original amount

e = Euler's number ≈ 2.71828

k = growth rate constant

t = time

Deriving a formula from this general formula to calculate for the time t:

y = aekt

y/a = ekt

Take the logarithms of both sides of the equation

log(y/a) = log(ekt)

Take down exponent kt as a coefficient

log(y/a) = (kt)log(e)

t = log(y/a)/klog(e)--> formula to solve for time t where y/a is the ratio of the final amount to the original amount

In the problem,

y/a = 2 (the ratio is 2 since the amount doubled)

k = 12% = 0.12

e = 2.71828

Using our derived formula:

t = log(y/a)/klog(e)

t = log(2)/(0.12)log(2.71828)

t = 5.7762 days