How do you work out this difficult word problem below?

Transylvania's fuelwood consumption, in millions of tons per year, is given by 90^e0.05t, where t is measured in years beginning with January 1, 1990. New tree growth is given by 160^e0.02t. During what year will consumption exceed production for the first time? Assume all figures are exact and don't round. -- (e0.05t %26amp; e0.02t) are both exponets.





a. 2006





b. 2007





c. 2009





d. 2018





e. 2030





f. 2047





or none of theseHow do you work out this difficult word problem below?
In order to solve this problem, you need to find out when these two quantities are equal to each other. After this time, then we know that consumption is greater than production.





Set these two equation equal to each other and solve for 't':





90*e^(0.05t) = 160*e^(0.02t) -----%26gt; Divide both sides by e^(0.02t)





90*e^(0.03t) = 160 ------%26gt; Divide by 90 and take natural log





0.03t = ln(160/90) -------%26gt; Divide by 0.03





t = [ln(160/90)]/(0.03) = 19.18 years





This means that consuption with exceed production 19 years after 1990. That would be the year 2009





The answer is C





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Hope this helps