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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 22 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.
L(t) = left parenthesis, t, right parenthesis, equals

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opudodennis

Answer:

[tex]L(t)=7600e^{0.2273t}[/tex]

Step-by-step explanation:

-The locust population grows by a factor and can therefore be modeled by an exponential function of the form:

[tex]P=P_oe^{rt}[/tex]

Where:

  • [tex]P[/tex] is the population after t days.
  • [tex]P_o[/tex] is the initial population given as 7600
  • [tex]r[/tex] is the rate of growth
  • [tex]t[/tex] is time in days

-Given that the growth is by a factor of 5( equivalent to 500%), the r value will be 5

-The population increases by a factor of 5 every 22 days. therefore at any time instance, t will be divided by 22 to get the effective time for calculations.

Hence, the exponential growth function will be expressed as:

[tex]P=P_oe^{rt},\ \ \ P=L(t)\\\\\therefore L(t)=7600e^{5\frac{t}{22}}\\\\=7600e^{0.2273t}[/tex]

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