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 nanorelated patents. Which expression gives the number of patents in 1998 ? Choose 1 answer: (A) 60*1.2^(7) (B) 60+(1+1.2)^(7) (C) 60*(1+1.2)^(7) (D) 60+1.2^(7)

Identify base and target years: Identify the base year and the target year to calculate the number of years over which the growth occurs. The base year is 1991, and the target year is 1998. To find the number of years between them, we subtract the base year from the target year. 1998 - 1991 = 7 yearsRecognize growth pattern: Recognize the growth pattern of the patents. The number of patents increases by a factor of 1.2 every year. This is an exponential growth pattern, which can be represented by the formula P(t) = P_0 * (growth factor)^(number of years), where P(t) is the number of patents at year t, P_0 is the initial number of patents, and the growth factor is 1.2.Apply exponential growth formula: Apply the exponential growth formula to find the expression for the number of patents in 1998. Using the initial number of patents P_0 = 60 and the growth factor of 1.2, we plug these values into the formula along with the number of years calculated in Step 1. P(1998) = 60 * 1.2^(7)Match obtained expression: Match the expression obtained with the given options. The expression we obtained is 60 * 1.2^(7), which corresponds to option (A).

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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 nanorelated patents.
Which expression gives the number of patents in 1998 ?
Choose 1 answer:
(A)
60*1.2^(7)
(B)
60+(1+1.2)^(7)
(C)
60*(1+1.2)^(7)
(D)
60+1.2^(7)

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 $60$ nanorelated patents. $\newline$ Which expression gives the number of patents in $1998$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $60 \cdot 1.2^{7}$ $\newline$ (B) $60+(1+1.2)^{7}$ $\newline$ (C) $60 \cdot(1+1.2)^{7}$ $\newline$ (D) $60+1.2^{7}$

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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

nanorelated patents.

\newline

Which expression gives the number of patents in

1998

\newline

Choose

1

answer:

\newline

(A)

60 \cdot 1.2^{7}

\newline

(B)

60+(1+1.2)^{7}

\newline

(C)

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

\newline

(D)

60+1.2^{7}

Identify base and target years: Identify the base year and the target year to calculate the number of years over which the growth occurs. $\newline$ The base year is $1991$ , and the target year is $1998$ . To find the number of years between them, we subtract the base year from the target year. $\newline$ $1998 - 1991 = 7$ years
Recognize growth pattern: Recognize the growth pattern of the patents. $\newline$ The number of patents increases by a factor of $1.2$ every year. This is an exponential growth pattern, which can be represented by the formula $P(t) = P_0 \times (\text{growth factor})^{(\text{number of years})}$ , where $P(t)$ is the number of patents at year $t$ , $P_0$ is the initial number of patents, and the growth factor is $1.2$ .
Apply exponential growth formula: Apply the exponential growth formula to find the expression for the number of patents in $1998$ . $\newline$ Using the initial number of patents $P_0 = 60$ and the growth factor of $1.2$ , we plug these values into the formula along with the number of years calculated in Step $1$ . $\newline$ $P(1998) = 60 \times 1.2^{7}$
Match obtained expression: Match the expression obtained with the given options. $\newline$ The expression we obtained is $60 \times 1.2^{7}$ , which corresponds to option (A).