Question

From $1970$ to $1980$, the rate of potato consumption in a particular country was $C\left(t\right)=2.2+{1.1}^t$ millions of bushels per year, with $t$ being years since the beginning of $1970.$ How many bushels were consumed from the beginning of $1972$ to the end of $1973$?

• A. $4.6$ million
• B. $\mathrm{6..2}$ million
• C. $7.066$ million
• D. $6.067$ million

Answer 1

Answer: (C)

$7.066$ million

Consuption =

${\int }_2^{4}C\left(t\right)dt\Rightarrow {\int }_2^4(2.2+1.1^t)dt\Rightarrow {[2.2t+\frac{{\left(1.1\right)}^t}{\ln \left(1.1\right)}]}_2^4\Rightarrow (2.2\times 4)+\frac{{\left(1.1\right)}^4}{\ln \left(1.1\right)}-(2.2\times 2)-\frac{{\left(1.1\right)}^2}{\ln \left(1.1\right)}=8.8-4.4+\frac{1.4641}{0.0965}-\frac{1.21}{0.095}$

$\Rightarrow 4.4+\frac{0.2541}{0.095}$

$\Rightarrow 4.4+2.67\Rightarrow 7.066$

Hence the correct answer is $7.066million$