**??? - 2016 JUNE Q8**

8.

i) The curve

ii) Alternatively, the curve

iii) Sketch the curve

iv) The point

v) Use the trapezium rule, with 2 strip each width of 1.5, to find an estimate for

i) The curve

*y*= 3^{ x }can be transformed to the curve*y*= 3^{ x+2 }by a translation. Give details of the translation [2]ii) Alternatively, the curve

*y*= 3^{ x }can be transformed to the curve*y*= 3^{ x+2 }by a stretch. Give details of the stretch. [2]iii) Sketch the curve

*y*= 3^{ x+2 }, stating the coordinates of any points of intersection with the axes. [2]iv) The point

*P*on the curve*y*= 3^{ x+2 }has the*y*coordinate equal to the 180. Use logarithms to find the*x*coordinate of*P*correct to 3 significant figures.v) Use the trapezium rule, with 2 strip each width of 1.5, to find an estimate for

Give your answer correct to 3 significant figures.