Consider the following function.

f(6) = 17, f'(6) = 8.2; x = 6.5

(a) Write a linearization for f with respect to x.

f_L(x) =

(b) Use the linearization to estimate f at the given input.

f_L(6.5) =

Consider the following function.

f(10) = 3, f'(10) = 0.4; x = 10.8

(a) Write a linearization for f with respect to x.

f_L(x) = (b) Use the linearization to estimate f at the given input.

f_L(10.8) =

The population of Mexico between 1921 and 2010 can be modeled as

p(t) = 8.028e^0.025t million people

where t is the number of years since 1900.

(a) What was the population of Mexico in 2007? (Round your answer to three decimal places.) _____ million people How rapidly was the population of Mexico growing in 2007? (Round your answer to three decimal places.) ______million people per year (b) Write a linearization of p in 2007. (Round all numerical values to three decimal places.)

p_L(t) =

(c) Use the linearization to estimate the population of Mexico in 2012. (Round your answer to three decimal places.) ______million people