Answer:
C. [tex]y=3\cdot 5^x[/tex]
Step-by-step explanation:
First two options show linear function and last two options show exponentioal functions. From the table you can see that
[tex]\dfrac{3}{5}=5\cdot \dfrac{3}{25}\\ \\3=5\cdot \dfrac{3}{5}\\ \\15=5\cdot 3\\ \\75=5\cdot 15[/tex]
This gives you that the function is exponential. Let the expression for the function be [tex]y=ab^x.[/tex] Substitute two values:
at x=0:
[tex]y=a\cdot b^0\\ \\3=a\cdot b^0\\ \\3=a\cdot 1\\ \\a=3[/tex]
at x=1:
[tex]y=a\cdot b^1\\ \\15=a\cdot b\\ \\15=3\cdot b\\ \\b=\dfrac{15}{3}\\ \\b=5[/tex]
Hence
[tex]y=3\cdot 5^x[/tex]
