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Jayden invested $1,500 in an account in the year 2005, and the value has been
growing exponentially at a constant rate. The value of the account reached $1, 800 in
the year 2011. Determine the value of the account, to the nearest dollar, in the year
2019.
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Answer 1

The value of the account in the year 2019 is approximately $2,169.

Step-by-step explanation:

To determine the value of the account in the year 2019, we can use the formula for exponential growth:

V = P(1 + r)^n

Where:
V is the value of the account in the year 2019
P is the initial investment ($1,500)
r is the growth rate (unknown)
n is the number of years (2019 - 2005 = 14)

Solving for r, we can rearrange the formula:
(1 + r)^n = V / P
1 + r = (V / P)^(1/n)
r = (V / P)^(1/n) - 1

Plugging in the given values:
r = (1800 / 1500)^(1/14) - 1

Calculating this expression, we find that r is approximately 0.04 (or 4%).

Finally, we can use the formula to determine the value of the account in 2019:
V = 1500(1 + 0.04)^14

Calculating this expression, we find that the value of the account in 2019 is approximately $2,169.