Question

The function n(w)=250 1.25^w represents the number of specialty items produced a the new factory w weeks after a change in management. The function p(w) = 70w +

320 represents the number of specialty items produced at the old factory in w weeks.

Explain the difference in the growth rates between the two functions. Determine the types of functions based on these rates

Answer 1

The growth rate of the function n(w) = 250 1.25^w is 25% per week, while the growth rate of the function p(w) = 70w + 320 is a fixed amount of 70 per week. n(w) is an exponential growth function, while p(w) is a linear growth function.

Step-by-step explanation:

The growth rates of the two functions can be determined by examining the constants in front of the variables. In the function n(w)=250 1.25^w, the growth rate is represented by the exponent, which is 1.25.

This means that for every week, the number of specialty items produced increases by 25%.

On the other hand, in the function p(w) = 70w + 320, the growth rate is represented by the coefficient of w, which is 70.

This means that for every week, the number of specialty items produced increases by a fixed amount of 70.

Based on these growth rates, the function n(w) = 250 1.25^w is an exponential growth function, because the output increases at an increasing rate over time. The function p(w) = 70w + 320 is a linear growth function, because the output increases at a constant rate over time.