A model for how long our coal resources will last is given by where r is the percent increase in consumption from current levels of use and T is the time (in years)before the resources are depleted. If our consumption of coal increases by 14% per year, in how many years will we deplete our coal resources?
A)88 years
B)14 years
C)29 years
D)67 years
E)39 years

Question

A model for how long our coal resources will last is given by  where r is the percent increase in consumption from current levels of use and T is the time (in years)before the resources are depleted. If our consumption of coal increases by 14% per year, in how many years will we deplete our coal resources?
A)88 years 
B)14 years 
C)29 years 
D)67 years 
E)39 years

Quizplus · Accepted Answer

The given model is 11ebfdc1_ec36_026a_abe3_dbf10f8287d6_TBX8727_11

T = (1/r) * ln(100/(100+r))

If consumption increases by 14% per year, r=14, then

T = (1/14) * ln(100/114) = 28.7 years

Thus, our coal resources will be depleted in approximately 29 years. The closest option is C (29 years).

A Model for How Long Our Coal Resources Will Last