Answer:
3. f(x) = 5^x
4. f(x) = 3 (8)^x
Step-by-step explanation:
3. Which function represents the data 2=>25, 3=>125, 4 =>625
You just have to plug the values of x in the equations provided and see which one fit, you stop testing for a given equation when it doesn't match the data table.
f(x) = x^4 + 9 - NO
for x = 2, 2^4 + 9 = 16 + 9 = 25 YES
for x = 3, 3^4 + 9 = 81 + 9 = 90 NO, should be 125
f(x) = 4^x + 9 - NO
for x = 2, 4^2 + 9 = 16 + 9 = 25 YES
for x = 3, 4^3 + 9 = 64 + 9 = 73 NO, should be 125
f(x) = x^5 - NO
for x = 2, 2^5 = 32 NO, should be 25
f(x) = 5^x YES
for x = 2, 5^2 = 25 YES
for x = 3, 5^3 = 125 YES
for x = 4, 5^4 = 625 YES
4. Which of the options is equivalent to f(x) = 3(2)^(3x)
By property of the powers you can easily break down the 3x exponent into a much simpler way.
[tex](2)^{3x} = (2^{3} )^{x} = 8^{x}[/tex]
From (2)^(3x) we got to 8^x, so the equation can now be written:
f(x) = 3 (8)^x, which is the first choice.
You could easily verify it with x = 2 in each equation.
