In the rectangle ABCD, AC=2x+19 and BD=5x-2. Find the value of x. Diagram is not drawn to scale
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Explanation:
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- <em>On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these flowers rapidly increases as the trees blossom. The locust population increases by a factor of 5 every 2 days, and can be modeled by a function, L, which depends on the amount of time, t (in days). Before the first day of spring, there were 7600 locusts in the population. Write a function that models the locust population t days since the first day of spring.</em>
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<h2>Solution</h2>A function that grows with a constant factor is modeled by an exponential function of the kind:
Where A is the initial value, B is the constant growing factor, and x is the number of times the growing factor applies.
Since the population increases by a factor of 5 every 2 days, the power x of the exponential function is t/2, and the factor B is 5.
The initial popultaion A is 7600.
Thus, the function that models the locust population t days since the first day of spring is: