the value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential growth model A= 6200e^(0.018(t)). When will the account be worth $9550?
To find the value of t when the account will be worth $9550, we need to solve the exponential equation A = 9550.
The exponential growth model is given by A = 6200e^(0.018t).
We can substitute A with 9550 in the equation, giving us:
9550 = 6200e^(0.018t)
To solve for t, we need to isolate the exponent term. Divide both sides of the equation by 6200:
9550/6200 = e^(0.018t)
Now, take the natural logarithm (ln) of both sides of the equation to get rid of the exponential term:
ln(9550/6200) = ln(e^(0.018t))
Using the property of logarithms that ln(a^b) = b * ln(a), the equation becomes:
ln(9550/6200) = 0.018t
Now, divide both sides of the equation by 0.018:
ln(9550/6200) / 0.018 = t
Using a calculator, evaluate the left side of the equation to find the approximate value of t.
just solve
9550 = 6500e^(.18t) for t years
t = 2.137 years from 2000
Just when the amount is reached depends on how often the increase is applied.