How do you write an exponential function of the form y = a b^x the graph of which passes through (-1, 4/5) and (2, 100)?

1 Answer
Jun 12, 2016

#y=4(5)^x#

Explanation:

Plug in #(x,y)=(-1,4/5)# and #(x,y)=(2,100)# to see the two equations that we're left with in terms of #a# and #b#.

For #(-1,4/5)#, we get

#4/5=a(b)^-1" "" "bb((1))#

and for #(2,100#) we get

#100=a(b)^2" "" "bb((2))#

Note that #bb((1))# can be rewritten as

#4/5=a/b" "" "bb((3))#

We can solve for #a# or #b#. Here, I'll solve for #a#.

#4/5b=a#

We can use #a=4/5b# to replace #a# with #4/5b# in #bb((2))#.

#100=a(b)^2" "=>" "100=4/5b(b)^2#

We can now solve this for #b#.

#100=4/5b^3#

Multiplying both sides by #5/4#:

#125=b^3#

#b=5#

Returning to #bb((3))# with our newfound value of #b#, we see that

#4/5=a/b" "=>" "4/5=a/5" "=>" "a=4#