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A population of 400 beetles grows by
5% each week. How can the beetle population be determined after a number of weeks,
w ?

A population of $400$ beetles grows by $5 \%$ each week. How can the beetle population be determined after a number of weeks, $w$ ?

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Write a linear function: word problems

Full solution

Q. A population of

400

beetles grows by

5 \%

each week. How can the beetle population be determined after a number of weeks,

w

?

Exponential Growth Formula: We know the population grows by $5\%$ each week. To find the population after $w$ weeks, we use the formula for exponential growth. $\newline$ Population after $w$ weeks = Initial population $\times (1 + \text{growth rate})^w$
Given Values: Initial population is $400$ beetles. $\newline$ Growth rate is $5\%$ , which is $0.05$ in decimal form. $\newline$ Number of weeks is $w$ . $\newline$ So, the equation is Population after $w$ weeks = $400 \times (1 + 0.05)^w$
Equation Setup: Now, we just plug in the value of $w$ to find the population after $w$ weeks. $\newline$ But since we don't have a specific value for $w$ , we leave the equation as is. $\newline$ Final equation: Population after $w$ weeks = $400 \times (1.05)^w$

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