Tim invest $5,000 in an account with a bank that offers an annual interest rate of 5%, compounded quarterly. Write the function that models the growth of a deposit of $5,000. A(t)= __(__+(__\__)) ^__t

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  A(t) = 5000(1 +.05/4)^(4t)

Step-by-step explanation:

The compound interest formula is ...

  A = P(1 +r/n)^(nt)

where principal P earns interest at annual rate r compounded n times per year for t years. The problem statement tells you P=5000, r=0.05, n=4. Putting these values into the formula gives ...

  A(t) = 5000(1 +0.05/4)^(4t)

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: