Carlos is investing money in a bank account where the value of his investment gr

Question

Carlos is investing money in a bank account where the value of his investment grows exponentially. One year after an investment was made the amount of money in the account was $2,025.50. Two years after the investment was made the amount of money in the account was $2,126.78. a. Determine the following: dollars Preview i. Initial value of the investment: 212678 ii. 1-year growth factor: I* Preview iii. 1-year percent change: Preview b. Define a function g that determines the value of the investment in terms of the number ofyears, t, since the investment was made. Preview c. Use your graphing calculator to determine after how many years the investment will be worth s5,000 (round to the nearest year). years Preview After

Explanation / Answer

From the given question,

A=p ert

t=1, A=$2025.50

2025.5=per ...................(1)

t=2, A=$2126.78

2126.78=pe2r...............(2)

dividing (2)/(1)

2126.78/2025.5=er

r=ln(2126.78/2025.5

r=0.0487

2025.5=per

p= 2025.5/(e0.0487)

p=$1929.2

initial value of investment= $1929.2

(ii) One year growth factor 4.8%

(iii)one year percentage change= (2025.5-1929.2)/(1929.2) x100

=5 %

(b) Value of investment t years later= 1929.2 e0.048t

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