What values of b0 produce a result within the desired tolerance? What is the input tolerance? Suppose

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What values of b0 produce a result within the desired tolerance? What is the input tolerance?
Suppose a population of bacteria follows the discrete-time dynamical system
bt+1 = 2.0bt
and we wish to have a population within 1.0 x 108 of 1.0 x 109 at t = 10.
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