Question

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

Answer 1

Answer:

$L(t)=7600e^{0.2273t}$

Step-by-step explanation:

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

$P=P_oe^{rt}$

Where:

• $P$ is the population after t days.
• $P_o$ is the initial population given as 7600
• $r$ is the rate of growth
• $t$ 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:

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