Question

I need help with my homework please check work when done I NEED HELP WITH THE QUESTION IN BLUE

Answer 1

Answer:
`f(x)=\text{ 4000\lparen}\frac{\text{ }x+\text{ 100}}{100})^{x\text{ +2}}\text{ }`

Step-by-step explanation:

Amount invested by Katelyn = $4000

rate = x%

time = x + 2 years

n = number of times compounded

n = annually = 1

We need to find the function that models the total amount

To find the function, we will apply the compound interest formula:

`\begin{gathered} $$FV\text{ = P(1 +}(r)/(n))^(nt)$$ \\ \\ P\text{ = 4000} \\ t\text{ = x + 2} \\ n\text{ = 1} \\ \text{ r = x\% = x/100} \\ FV=\text{ total amount } \end{gathered}`

substitute the values into the formula:

`\begin{gathered} FV=\text{ 4000\lparen 1 + }((x)/(100))/(1))^{1*(x\text{ + 2\rparen}} \\ \\ FV=\text{ 4000\lparen1 + }(x)/(100))^(x+2) \end{gathered}`
`FV=\text{ 4,000\lparen}\frac{100+\text{ }x}{100})^{x\text{ +2}}\text{ }`

let the function that represents the total amount = f(x)

`f(x)=\text{ 4000\lparen}\frac{\text{ }x+\text{ 100}}{100})^{x\text{ +2}}\text{ }`