If a state issued license plates using the scheme of 3 letters followed by 3 digits, how many plates could it issue?
1 answer:
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For the first point, remember this simple rule: every exponential function always returns
when evaluated at
. In fact,
for every possible base
.
So, we can see that the graph of the exponential passes through the point where
appears to be between 1 and 2. So, the only feasible option would be
, because it passes throught the point
because
.
The other functions are wrong because:
would pass through
, which would be between 0 and 1 on the y axis
would pass through
, which would be between 2 and 3 on the y axis
would pass through
, which would be between 0 and 1 on the y axis
As for the second question, you simply have to plug in the values: the function
means that you have to choose an input, x, and use it as exponent for 7. So, if you choose x=2, it means that you have to give exponent 2 to 7, i.e. you replace the x with the specific value, 2.
So, the expression becomes