Question

In: Advanced Math

After the Introduction of a new product, the percent of the public that is aware of...

After the Introduction of a new product, the percent of the public that is aware of the product is approximated by

A(t)= 10t²2^-t

where t is time in months.

(a). Calculate A'(t).

(b). Find the rate of change of the percent of the public that is aware of the product after 2 months and after 4 months and include units.

(c). In part (b), one of your answers should have been positive while the other should have been negative. what dose that tell you about how the public awareness of the product has changed?

Expert Solution

to find the rate of change take derivative

apply product rule of derivative

.

.put t=2 months

percent of the public per month

.

.put t=4 months

percent of the public per month
.

.

here we have

here positive sign indicates increasing rate

so after 2 months percent of the public aware of the product is increasing

.

here we have

here negative sign indicates decreasing rate

so after 4 months percent of the public aware of the product is decreasing

Colby Messinger answered 2 years ago

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