How does f(t) = 2^t change over the interval from t = 1 to t = 2? Choices: (A)f(t) decreases by 2% (B)f(t) increases by 200% (C)f(t) increases by a factor of 2 (D)f(t) increases by 2

Calculate f(t): Calculate f(t) when t = 1. f(1) = 2^1 = 2.Calculate f(t): Calculate f(t) when t = 2. f(2) = 2^2 = 4.Compare values: Compare f(2) to f(1) to find the change. The change is 4 - 2 = 2.Determine percentage increase: Determine the percentage increase from f(1) to f(2). Percentage increase = (Change / Original value) * 100% = (2 / 2) * 100% = 100%.

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How does $f(t) = 2^t$ change over the interval from $t = 1$ to $t = 2$ ? $\newline$ Choices: $\newline$ (A) $f(t)$ decreases by $2\%$ $\newline$ (B) $f(t)$ increases by $200\%$ $\newline$ (C) $f(t)$ increases by a factor of $2$ $\newline$ (D) $f(t)$ increases by $2$

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Math Problems

Calculus

Find derivatives using the product rule II

Full solution

Q. How does

f(t) = 2^t

change over the interval from

t = 1

t = 2

\newline

Choices:

\newline

(A)

f(t)

decreases by

2\%

\newline

(B)

f(t)

increases by

200\%

\newline

(C)

f(t)

increases by a factor of

2

\newline

(D)

f(t)

increases by

2

Calculate $f(t)$ : Calculate $f(t)$ when $t = 1$ . $\newline$ $f(1) = 2^1 = 2$ .
Calculate $f(t)$ : Calculate $f(t)$ when $t = 2$ . $\newline$ $f(2) = 2^2 = 4$ .
Compare values: Compare $f(2)$ to $f(1)$ to find the change. $\newline$ The change is $4 - 2 = 2$ .
Determine percentage increase: Determine the percentage increase from $f(1)$ to $f(2)$ . $\newline$ Percentage increase = $\frac{\text{Change}}{\text{Original value}} \times 100\% = \frac{2}{2} \times 100\% = 100\%$ .