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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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Write exponential functions: word problems

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

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).

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