The number of nano-related patents that are granted in the US increases by a factor of $1$ . $2$ every year. In $1991$ , there were $60$ nano-related patents. $\newline$ Which expression gives the number of patents in $1998 ?$ $\newline$ Choose $1$ answer: $\newline$ (A) $60+(1+1.2)^{7}$ $\newline$ (B) $60 \cdot 1.2^{7}$ $\newline$ (C) $60+1.2^{7}$ $\newline$ (D) $60 \cdot(1+1.2)^{7}$

Full solution

Q. The number of nano-related patents that are granted in the US increases by a factor of

1

2

every year. In

1991

, there were

60

nano-related patents.

\newline

Which expression gives the number of patents in

1998 ?

\newline

Choose

1

answer:

\newline

(A)

60+(1+1.2)^{7}

\newline

(B)

60 \cdot 1.2^{7}

\newline

(C)

60+1.2^{7}

\newline

(D)

60 \cdot(1+1.2)^{7}

Understand the problem: Understand the problem. $\newline$ We need to find the expression that represents the growth of the number of patents from $1991$ to $1998$ . The growth is exponential, with a factor of $1.2$ each year.
Calculate years: Calculate the number of years from $1991$ to $1998$ . $\newline$ $1998 - 1991 = 7$ years
Apply growth formula: Apply the exponential growth formula. $\newline$ The number of patents in a given year is the initial number of patents multiplied by the growth factor raised to the number of years that have passed. $\newline$ Number of patents = Initial patents $\times$ (Growth factor) $^{\text{Number of years}}$
Substitute values: Substitute the given values into the formula. $\newline$ Initial patents = $60$ $\newline$ Growth factor = $1.2$ $\newline$ Number of years = $7$ $\newline$ Number of patents = $60 \times (1.2)^{7}$
Identify correct expression: Identify the correct expression from the choices. $\newline$ The correct expression that matches our formula is $(B) 60\times1.2^{7}$ .