Write an exponential function for graph that passes through the following points (-3,80);(-1,20)

Accepted Solution

Answer:y=4(12)xExplanation:An exponential function is in the general formy=a(b)xWe know the points(βˆ’1,8)and(1,2), so the following are true:8=a(bβˆ’1)=ab2=a(b1)=abMultiply both sides of the first equation bybto find that8b=aPlug this into the second equation and solve forb:2=(8b)b2=8b2b2=14b=Β±12Two equations seem to be possible here. Plug both values ofbinto the either equation to finda. I'll use the second equation for simpler algebra.Ifb=12:2=a(12)a=4Giving us the equation:y=4(12)xIfb=βˆ’12:2=a(βˆ’12)a=βˆ’4Giving us the equation:y=βˆ’4(βˆ’12)xHowever! In an exponential function,b>0, otherwise many issues arise when trying to graph the function.The only valid function isy=4(12)x