Question

Good Afternoon I have a couple of problems I need help one. Can someone help on this ASAP. (It would be greatly appreciated if you showed your work)

Thank you have a good day

Answer 1

C.
`y=3\cdot 5^x`

Explanation:

First two options show linear function and last two options show exponentioal functions. From the table you can see that

`(3)/(5)=5\cdot (3)/(25)\\ \\3=5\cdot (3)/(5)\\ \\15=5\cdot 3\\ \\75=5\cdot 15`

This gives you that the function is exponential. Let the expression for the function be
`y=ab^x.` Substitute two values:

at x=0:

`y=a\cdot b^0\\ \\3=a\cdot b^0\\ \\3=a\cdot 1\\ \\a=3`

at x=1:

`y=a\cdot b^1\\ \\15=a\cdot b\\ \\15=3\cdot b\\ \\b=(15)/(3)\\ \\b=5`

Hence

`y=3\cdot 5^x`