# Exponents in word

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**Description:** A list of Exponents word problems.

Exponentiation is a mathematical operation, written a n. involving two numbers, the base a and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication: a 1 = a a 2 = a × a a 3 = a × a × a a 4 = a × a × a × a and so on.

The rat population in a major metropolitan city is given by the formula n(t)= 73 e 0.015 t where t is measured in years since 1990 and n(t) is measured in millions. What was the rat population in 1990. What is the rat population going to be in the year 2005.

An advertising company designs a campaign to introduce a new product to a metropolitan area of population M = 3 millions. Let P = P(t) denote the number of people who become aware of the product by time t. Suppose that P increases at a rate proportional to the number of people still unaware of the product. The company determines that no one is aware of the product at the beginning of the campaign and that 40% of the people were aware of the product after 10 days of advertising. Give the differential equation that describes the number of people who become aware of the product by time t.