On the first day of winter, an entire field of trees starts losing its flowers. The number of locusts remaining alive in this population decreases rapidly due to the lack of flowers for them to eat. $\newline$ The relationship between the elapsed time, $t$ , in days, since the beginning of winter, and the total number of locusts, $N(t)$ , is modeled by the following function: $\newline$ $N(t)=8950 \cdot(0.49)^{\frac{t}{2}}$ $\newline$ Complete the following sentence about the daily rate of change in the locust population. $\newline$ Round your answer to two decimal places. $\newline$ Every day, the locust population is multiplied by a factor of

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Q. On the first day of winter, an entire field of trees starts losing its flowers. The number of locusts remaining alive in this population decreases rapidly due to the lack of flowers for them to eat.

\newline

The relationship between the elapsed time,

t

, in days, since the beginning of winter, and the total number of locusts,

N(t)

, is modeled by the following function:

\newline

N(t)=8950 \cdot(0.49)^{\frac{t}{2}}

\newline

Complete the following sentence about the daily rate of change in the locust population.

\newline

Round your answer to two decimal places.

\newline

Every day, the locust population is multiplied by a factor of

Identify Function: Identify the function that models the locust population over time. $\newline$ $N(t) = 8950 \times (0.49)^{\frac{t}{2}}$
Determine Daily Rate: Determine the factor by which the population changes each day. This is the base of the exponent, raised to the power of $\frac{1}{2}$ , since $t$ is in days and we want the daily rate. $\newline$ Daily rate of change factor = $(0.49)^{\frac{1}{2}}$
Calculate Rate Factor: Calculate the daily rate of change factor using a calculator or appropriate software. $\newline$ Daily rate of change factor $\approx (0.49)^{\frac{1}{2}} \approx 0.7$
Round to Two Decimals: Round the daily rate of change factor to two decimal places. $\newline$ Daily rate of change factor $\approx 0.70$