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Maths-

SAT

Easy

Question

The half-life of a certain substance in an aquatic environment is about 150 years. Which of the following exponential functions best models the amount A(t), in grams, of the substance t years after 200 grams of the substance is applied to the aquatic environment? (The half-life is the length of time needed for an amount of the substance to decrease to one-half of that amount.)

$A (t) = 150 {(\frac{1}{2})}^{\frac{t}{200}}$
$A (t) = 150 {(\frac{1}{2})}^{200 t}$
$A (t) = 200 {(\frac{1}{2})}^{150 t}$
$A (t) = 200 {(\frac{1}{2})}^{\frac{t}{150}}$

The correct answer is: $A left parenthesis t right parenthesis equals 200 open parentheses 1 half close parentheses to the power of t over 150 end exponent$

The half - life is the time needed for an amount of the substance to decrease to one - half of the amount.
Given, half - life of certain substance is 150 years.
The amount in grams of substance is 200.
$A open parentheses t close parentheses equals open parentheses T o t a l space a m o u n t close parentheses space open parentheses h a l f close parentheses to the power of fraction numerator t over denominator h a l f minus l i f e space p e r i o d end fraction end exponent equals open parentheses 200 close parentheses open parentheses 1 half close parentheses to the power of t over 150 end exponent$

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