Answer:
L(t) = 1100(1.87)^(t/2.4)
Corrected 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 gains 0.87 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.
Explanation:
Given;
Initial amount P = 1100
Rate of growth r = 87% = 0.87
Time step k = 2.4 days
The case above can be represented by an exponential function;
L(t) = P(1+r)^(t/k)
Where;
L(t) = locust population at time t days after the first day of spring
P = initial locust population
r = rate of increase
t = time in days
k = time step
Substituting the given values;
L(t) = 1100(1+0.87)^(t/2.4)
L(t) = 1100(1.87)^(t/2.4)
the locust population t days since the first day of spring can be modelled using the equation;
L(t) = 1100(1.87)^(t/2.4)