Question

the expression $60cdot1.2^t$ models the number of nano - related patents granted in the us as a function of years since 1991. what does 60 represent in this expression? choose 1 answer: a the first nano - related patents were granted 60 years before 1991. b there were 60 nano - related patents granted in 1991. c the number of nano - related patents granted is multiplied by 60 each year.

Explanation:

The expression \( 60 \cdot 1.2^{t} \) is an exponential model, where \( t \) is the number of years since 1991. In an exponential function of the form \( P(t)=a\cdot b^{t} \), \( a \) represents the initial value (when \( t = 0 \)). When \( t = 0 \) (which corresponds to the year 1991), the expression becomes \( 60\cdot1.2^{0}=60\cdot1 = 60 \). So, 60 represents the number of nano - related patents in 1991.

• Option A is incorrect because the model is about years since 1991, and 60 has no relation to years before 1991 in this context.
• Option C is incorrect because the growth factor is 1.2 (the number of patents is multiplied by 1.2 each year, not 60).

Answer:

B. There were 60 nano - related patents granted in 1991.