# quiz7

$~Which~arguments~are~true~about~the~function~y=(1+\frac{1}{n})^{n}?$

$Which~of~the~following~arguments~are~true~both~for~y=10^{x}~and~y=e^{x}?$

$Suppose~a~country's~GDP~grows~at~3%~p.a.~continuously,~rather~than~growing~at~3%~from~the~previous~year.~The~country's~GDP~is~142~billion~GBP~in~2000.~$$Find~the~equation~which~describes~the~trajectory~of~y,~the~GDP~(GBP),~x~years~later.$

$Suppose~the~interest~is~added~continuously~at~5%~p.a.~What~is~the~effective~annual~interest~rate~(APR)?$

$Suppose~the~interest~is~added~continuously~added~at~5%~p.a.~How~long~does~it~take~for~the~future~compounded~value~to~be~twice~larger~$$than~the~original~investment?$

$Suppose~the~interest~is~added~continuously~added~at~5%~p.a.~You~invest~100~GBP~now,~and~what~will~be~the~future~value~after~5~years~and~27~days?$

$The~GDP~of~a~country~grows~continuously~at~5%~p.a.~so~that~GDP~=~GDP_{0}\cdot~e^{0.05x},~where~GDP_{0}~is~GDP~at~year~0,~and~x~refers~to~the~year.~$$~How~much~does~the~economy~grow~for~one~year?$

$~Find~the~inverse~function~of~y=e^{0.1x}$

$There~is~a~kind~of~radioactive~material.~The~material's~radioactivity~depreciate~0.1%~p.a.~How~much~percentage~of~the~radioactivity~will~remain~$$1000~years~later?$

$There~is~a~kind~of~radioactive~material.~The~material's~radioactivity~continuously~depreciate~0.1%~p.a.~How~long~does~it~take~for~the~radioactivity~$$to~be~halved?$

$The~book~value~of~a~sort~of~machine~is~supposed~to~depreciate~at~5%~p.a.~according~to~the~account~rule.~What~will~be~the~book~value~of~the~machine~20~$$years~after~purchase?$

$The~book~value~of~a~sort~of~machine~is~supposed~to~depreciate~at~5%~p.a.~according~to~the~account~rule.~How~long~does~it~take~for~the~book~value~of~the~$$machine~to~be~halved?$

Find the inverse function of $~y=100e^{-0.05x}$

$~Find~the~inverse~function~of~y=10\ln~x.$

$There~is~a~economy~with~the~debt/GDP~ratio~of~80%.~The~country~has~reached~a~balanced~budget,~and~the~level~of~debt~remains~constant.~The~GDP~$$is~growing~at~3%~p.a.~continuously~(not~discretely~between~the~end~of~years).~How~long~does~it~take~for~the~ratio~to~fall~below~60%?$

$Find~correct~arguments~about~the~natural~log~of~the~GDP~of~a~country.$

$The~population~of~a~country~is~growing~at~1.5%~p.a.,~and~the~population~is~growing~continuously~at~constant~rate.~Using~"the~rule~of~69",~approximately~$$find~how~long~does~it~take~for~the~population~to~be~doubled.$

$The~inflation~rate~of~an~economy~is~at~3%~p.a.,~and~the~price~level~is~rising~continuously~at~constant~rate.~Using~"the~rule~of~69",~approximately$$~find~how~long~does~it~take~for~the~real~value~of~the~currency~to~be~halved.~$
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