3. Một Thư Viện Có 960 Cuốn Truyện Tranh - Gauthmath

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Question

A mug of warm apple cider is gradually cooling. Its temperature in degrees Celsius (^circ C) can be modeled with the expression 23+24· 2^(-0.014t), where the variable t represents the time in minutes. Approximately how many minutes will it take for the temperature to reach 29°C 7SHOW LESS169

Solution

user avatar imageAnswer The answer is **143 minutes**ExplanationStep 1: **Equate the temperature expression to the target temperature.** We set the given expression for the temperature of the apple cider equal to 29°C: $23 + 24 \cdot 2^{-0.014t} = 29$ Step 2: **Isolate the exponential term.** Subtract 23 from both sides of the equation: $24 \cdot 2^{-0.014t} = 6$ Divide both sides by 24: $2^{-0.014t} = \frac{6}{24} = \frac{1}{4}$ Step 3: **Express the equation in logarithmic form.** Since $\frac{1}{4} = 2^{-2}$, we can rewrite the equation as: $2^{-0.014t} = 2^{-2}$ Step 4: **Solve for t.** Equating the exponents, we get: $-0.014t = -2$ Dividing both sides by -0.014: $t = \frac{-2}{-0.014} \approx 142.86$ Step 5: **Interpret the result.** The time $t$ represents the time in minutes. Rounding to the nearest minute, it will take approximately 143 minutes for the temperature to reach 29°C. Click to rate:40.3(62 votes)Search questionBy textBy image/screenshotDrop your file here orClick Hereto upload

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