# The graph #y=ab^x# passes through #(2, 400)# and #(5,50)#. Find values for #a# and #b#, and, given that #ab^x>k# for some constant #k>0#, show that #x>log(1600/k)/log2# where log means log to any base?

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I am very confident that #b=1/2# and #a=1600# but I'm not sure how to go about this proof. Thanks!

I am very confident that

##### 2 Answers

Please see below.

#### Explanation:

As

Dividing latter by former, we get

As such

and hence

Let for some

then

or

or

or

i.e.

or

Given

So

and

Dividing (2) by (1) we get

Inserting the value of b in (1) we get

Now