Question

Please help with the bonus! Thank you:)

Answer 1

a. The function that models the situation is  F(t) = 48(1.08)ˣ

b. The price of the stock 6 years from now is $76.17

c. Find the graph in the attachment

d. I receive a dividend of $0.026.

a. Write a function f(t) that models the situation.

Since the stock price increases at a rate of 8% every year, and is initially $48, it follows exponential growth.

So, the current price $F(t) = A(1 + r)^{t}$ where

• A = price at current moment = $48,
• r = rate of growth = 8% = 0.08 and
• t = number of years

So,  $F(t) = A(1 + r)^{t}$

$F(t) = 48(1 + 0.08)^{t} \\= 48(1.08)^{t}$

So, the function that models the situation is F(t) = 48(1.08)ˣ

b. Determine the price of the stock 6 years from now?

The price of the stock 6 years from now is gotten when t = 6.

So,

$F(t) = 48(1.08)^{t} \\= 48(1.08)^{6} \\= 48(1.5869)\\= 76.17$

So, the price of the stock 6 years from now is $76.17

c. Sketch a graph of the price of the function vs time in years

Find the graph in the attachment

d. Bonus

Since every quarter, the company pays a dividend of 1.5 %, the rate per year would be r = 1.5 % ÷ 1/4 year = 1.5 % × 4 = 6 % per year.

Since they pay at a rate, r = 6 % = 0.06 of the stock price, F(t) as dividend.

After n years, the dividend is D = (r)ⁿF(t)

= (0.06)ⁿF(t)

So, $D = (0.06)^{t}F(t) \\= (0.06)^{t}[4.8(1.08)^{t}]$

So, after 3 years when t = 3,

$D = (0.06)^{t}[4.8(1.08)^{t}]\\D = (0.06)^{3}[4.8(1.08)^{3}]\\D = 0.000216 \times 48 \times 1.2597\\D = 0.013$

Since there are 3 shares, the total dividend would be D' = 3D

= 3 × 0.013

= 0.026

So, i receive a dividend of $0.026

Learn more about exponential function here:

brainly.com/question/12940982

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