The amount of coffee consumed annually in Country X increases by 8 percent each year. If 970 thousand metric tons of coffee were consumed in 2000, which of the following functions c can be used to model the amount of coffee, in thousands of metric tons, consumed annually in Country X, where t is the number of years since 2000?

This linear function suggests a constant increase of 1.08 thousand metric tons each year, failing to account for the compounding growth of coffee consumption. Since the problem specifies an 8 percent annual increase, the consumption grows exponentially rather than linearly.

While this function uses the correct initial amount of 970, it incorrectly multiplies by 1.08 raised to the power of t in a non-exponential context. This expression would suggest a linear growth pattern, which does not reflect the compounding nature of the coffee consumption increase described in the question.

This function proposes that consumption is based on 970 raised to the power of 1.08 multiplied by t, which misrepresents the relationship between time and coffee consumption. It does not reflect the compounding growth but rather suggests a fixed initial amount raised to a power, which does not apply in this scenario.

This function also implies a polynomial increase based on time, suggesting that coffee consumption grows by a factor of t raised to a power rather than exhibiting the necessary exponential growth. It fails to incorporate the correct compounding factor of 1.08 as a base raised to the power of t.