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Fidel has a rare coin worth
$550. Each decade, the coin's value increases by
10%.
Which kind of function best models the relationship between time and the coin's value?
Choose 1 answer:
(A) Linear
(B) Exponential

Fidel has a rare coin worth $\$ 550$ . Each decade, the coin's value increases by $10 \%$ . $\newline$ Which kind of function best models the relationship between time and the coin's value? $\newline$ Choose $1$ answer: $\newline$ (A) Linear $\newline$ (B) Exponential

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Identify linear and exponential functions from word problem

Full solution

Q. Fidel has a rare coin worth

\$ 550

. Each decade, the coin's value increases by

10 \%

.

\newline

Which kind of function best models the relationship between time and the coin's value?

\newline

Choose

1

answer:

\newline

(A) Linear

\newline

(B) Exponential

Identify Type Increase: Identify the type of increase in the coin's value. $\newline$ The coin's value increases by $10\%$ each decade, which means the increase is a percentage of the current value. This is characteristic of exponential growth, not a constant addition.
Determine Function Type: Determine the type of function that models exponential growth. $\newline$ Since the value increases by a percentage (multiplicative change) rather than a fixed amount (additive change), the function that models this situation is an exponential function.
Choose Correct Answer: Choose the correct answer based on the type of function identified. $\newline$ The correct answer is (B) Exponential, as the coin's value increases by a percentage each decade.

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