How do you solve for t in $44 = 2, 500 \times {0.5}^{\frac{t}{5.95}}$ $44=2,500times0.5^(t/5.95)$ ?

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How do you solve for t in $44 = 2, 500 \times {0.5}^{\frac{t}{5.95}}$ $44=2,500times0.5^(t/5.95)$ ?

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Answer 1 · 2016-05-14T04:39:09

$t \approx 34.68$ $t~~34.68$

Explanation:

Given,

$44 = 2500 \cdot {0.5}^{\frac{t}{5.95}}$ $44=2500*0.5^(t/5.95)$

Divide both sides by $2500$ $2500$ .

$\frac{44}{2500} = {0.5}^{\frac{t}{5.95}}$ $44/2500=0.5^(t/5.95)$

Take the logarithm of both sides since the bases are not the same.

$log (\frac{44}{2500}) = log ({0.5}^{\frac{t}{5.95}})$ $log(44/2500)=log(0.5^(t/5.95))$

Using the logarithmic property, ${log}_{b} (x^{y}) = y \cdot {log}_{b} (x)$ $log_color(purple)b(color(blue)x^color(red)y)=color(red)y*log_color(purple)b(color(blue)x)$ , the equation becomes,

$log (\frac{44}{2500}) = (\frac{t}{5.95}) log (0.5)$ $log(44/2500)=(t/5.95)log(0.5)$

$log (\frac{44}{2500}) = \frac{log (0.5)}{5.95} \cdot t$ $log(44/2500)=log(0.5)/5.95*t$

Solve for $t$ $t$ .

$t = \frac{log (\frac{44}{2500})}{\frac{log (0.5)}{5.95}}$ $t=log(44/2500)/(log(0.5)/5.95)$

$t = \frac{5.95 log (\frac{44}{2500})}{log (0.5)}$ $t=(5.95log(44/2500))/(log(0.5))$

$color(green)(|bar(ul(color(white)(a/a)color(black)(t~~34.68)color(white)(a/a)|)))$

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How do you solve for t in $44 = 2, 500 \times {0.5}^{\frac{t}{5.95}}$ $44=2,500times0.5^(t/5.95)$ ?

1 Answer

Explanation:

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How do you solve for t in 44=2,500times0.5^(t/5.95)44=2,500×0.5t5.9544=2,500times0.5^(t/5.95)?

1 Answer

Explanation:

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How do you solve for t in $44 = 2, 500 \times {0.5}^{\frac{t}{5.95}}$ $44=2,500times0.5^(t/5.95)$ ?