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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 gains
87% of its size every 2.4 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 1100 locusts in the population.
Write a function that models the locust population
t days since the first day of spring.

L(t)=

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 gains $87 \%$ of its size every $2$ . $4$ days, and can be modeled by a function, $L$ , which depends on the amount of time, $t$ (in days). $\newline$ Before the first day of spring, there were $1100$ locusts in the population. $\newline$ Write a function that models the locust population $t$ days since the first day of spring. $\newline$ $L(t)=$

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Write exponential functions: word problems

Full solution

Q. 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 gains

87 \%

of its size every

2

.

4

days, and can be modeled by a function,

L

, which depends on the amount of time,

t

(in days).

\newline

Before the first day of spring, there were

1100

locusts in the population.

\newline

Write a function that models the locust population

t

days since the first day of spring.

\newline

L(t)=

Identify values: Identify the initial value $a$ and the growth rate $r$ . The initial value, $a$ , is the starting population of locusts, which is $1100$ . The growth rate, $r$ , is $87$ \%, which can be expressed as a decimal $0.87$ .
Determine growth factor: Determine the growth factor $b$ . Since the population increases by $87\%$ , the growth factor $b$ is $1$ plus the growth rate. $b = 1 + r$ $b = 1 + 0.87$ $b = 1.87$
Determine time period: Determine the time period for the growth rate. $\newline$ The problem states that the population gains $87\%$ every $2.4$ days. Therefore, the growth factor applies every $2.4$ days.
Write exponential function: Write the exponential function. $\newline$ The exponential function for growth is $L(t) = a(b)^{(t/k)}$ , where $k$ is the time period for each growth cycle. $\newline$ In this case, $k = 2.4$ days. $\newline$ So, the function becomes $L(t) = 1100(1.87)^{(t/2.4)}$ .

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