Question

# A useful concept in mathematical growth models is that of the doubling time, defined as the...

1. A useful concept in mathematical growth models is that of the doubling time, defined as the time required for an initial value ( i.e population) to double
1. Derive a general expression that can be used to find the doubling time , t2x , for a given exponential growth rate , r.
2. Use this expression to find the growth rate that will cause a population to double in 10 years
1. It has been proposed to increase the average fuel economy of new cars from the current standard of 27.5 miles per gallon (mpg) to 32.5 mpg in order to reduce energy consumption and lower the CO2 emissions of the fleet by 15 percent. If the new mpg standard was enacted, but new car production continued to grow at a compound annual rate of 2.4 percent/year ( with no chance in the annual miles driven per vehicle), how many years would it take for the increased number of new cars to wipe out the CO2 reduction achieved by the first 32.5 mpg fleet ?

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