# Tutor profile: Uddhav G.

## Questions

### Subject: Calculus

Solve the following: $$ \int_2^\5 \mathrm{e}^{2x},\mathrm{d}x $$

First integrate the expression $$e^{2x}$$, which results in $$frac{e^{2x}}{2}$$ The result has the lower bound of 2 and the upper bound of 5. (1) -- Substituting x for the upper bound results in 11,013 (2) -- Substituting x for the lower bound results in 27 Subtracting (2) from (1) -> 11,013-27 = 10,986

### Subject: English as a Second Language

It was a lovely, sunny afternoon. Jane _____ hard to finish her homework quickly so that she _____ go out to play. Fill in the blanks with the most suitable answers: A) worked, can B) worked, could C) works, can D) works, could

Answer: B WORKED: past tense of WORK COULD: past tense of CAN While option C may seem reasonable, bear in mind that the first sentence sets the scene in the past.

### Subject: Economics

In a hypothetical situation, an economy exists for only 2 years. It produces two products in these two years: motorbikes and cars. In year 1, 1,000 motorbikes are sold at $3,000 each, and 500 cars are sold at $10,000 each. In year 2, 1,100 motorbikes are sold at $3,100 each, and 450 cars are sold at $12,000 each. a) Calculate the nominal GDP in years 1 and 2. b) Calculate the real GDP for both years, with year 1 acting as the base year. c) Work out the implicit price deflator for both years. d) What are the growth rates of real output and prices?

a) $$ NominalGDP_1 = 1,000*$3,000 + 500*$10,000$$ $$ = $8,000,000 $$ $$ NominalGDP_2= 1,100*$3,100 + 450*$12,000$$ $$ = $8,810,000 $$ b) $$ RealGDP_1 = 1,000*$3,000 + 500*$10,000$$ $$ = $8,000,000 $$ $$ RealGDP_2= 1,100*$3,000 + 450*$10,000$$ $$ = $7,800,000 $$ c) The implicit price deflator is the given by: $$ P_t^b = \frac{NominalGDP}{RealGDP} $$ Where $$ t $$ is the given year, and $$ b $$ is the base year $$ P_1^1 = \frac{$8,000,000}{$8,000,000} *100 $$ $$=100$$ $$ P_2^1 = \frac{$8,810,000}{$7,800,000} *100 $$ $$=112.95$$ d) The growth rate of real output, $$g^y$$, is the change in the real GDP between the years: $$g^y=\frac{7,800,000-8,000,000}{8,000,000}*100\%$$ $$g^y=-0.025 \% $$ The growth rate of real prices is simply equivalent to inflation, $$\pi$$, which can be found from the change in the implicit price deflator $$\pi=\frac{112.95-100}{100}*100\%$$ $$\pi=12.95 \% $$

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