To find the exponential function for the graph, we need to determine the equation in the form y = ab^x, where y is the value of the boat, x is the number of years, a is the initial value of the boat, and b is the decay factor.
From the given information, we know that the boat starts at a value of $3500 when x = 0. Therefore, a = 3500.
Also, we know that the boat passes through the point (1, 2700). Plugging these values into the exponential function equation, we get:
2700 = 3500 * b^1
Simplifying, we divide both sides by 3500:
b = 2700/3500
b ≈ 0.7714
So, the exponential function for the graph is:
y = 3500 * 0.7714^x
Now, we can find the value of the boat after 9.5 years by plugging x = 9.5 into the equation:
y = 3500 * 0.7714^9.5
y ≈ 2079.79
Therefore, the value of the boat after 9.5 years is approximately $2079.79.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years.
A coordinate graph is shown. The horizontal axis extends from 0 to 12 years. The vertical axis extends from 0 to 9500 with an axis label of 'Value' in dollars. A curve is graphed which begins at 0 comma 3500, then decreases passing through approximately 1 comma 2700
Write an exponential function for the graph. Use the function to find the value of the boat after 9.5 years.
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