Question

1. Dylan invested $47,000 in an account paying an interest rate of 4% compounded annually. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $79,200?

2. x^2 + y^2 = 153 and y = -4x. If (x, y) is a solution to the system of equations above, what is the value of y^3?

Answer 1

13.3

Explanation:

I got it right

Answer 2

(1) 13.0 years

(2)
`y^(3) =` {-1728, 1728}

Explanation:

(1)

Compound annually:

`Pe^(rt)` = A

(47000)
`e^((0.04)(t))` = 79200

`e^((0.04)(t))` =
`(79200)/(47000)`

ln(
`e^((0.04)(t))`) = ln(
`(79200)/(47000)`)

ln and e cancel out.

(0.04)(t) = ln(
`(79200)/(47000)`)

t =
`(ln((79200)/(47000)))/(0.04)`

t = 13.0 years

(2)

`x^(2) +y^(2) = 153\\y = -4x`

Substitute y with -4x.

`x^(2) + (-4x)^(2) = 153`

Solve for x.

x = {-3, 3}

Plug in x values into any equation to find y.

y = -4(-3) and y = -4(3)

y = {-12, 12}

`y^(3)` =
`-12^(3)` = -1728

`y^(3)` =
`12^(3)` = 1728