Rewriting Exponential Functions

Question 1

Combine the first two equations and laws of exponents to find the equation for the mass of sodium remaining after y years.

Revolt · Accepted Answer

S = 800(0.766)y

Question 2

Approximately how many milligrams of sodium remain after 8.4 years? 85.2 mg95.2 mg247.6 mg645.5 mg

Revolt · Accepted Answer

85.2 mg

Question 3

Choose the pair of expressions that describe the accounts y years after Martin opened his account.

Revolt · Accepted Answer

Martin: 200(1.05)y Cary: 200(1.05)y–4

Question 4

Which expression represents the mass of sodium remaining after h half-lives?

Revolt · Accepted Answer

S = 800(0.5)h

Question 5

Is this exponential growth or decay? Explain using your understanding of the properties of exponents. (To type exponents, use the ^ key.)

Revolt · Accepted Answer

This is exponential decay. The negative exponent means the base is reciprocated, so N(t) = 300 · (1/2)^(t/8) = 300 · 0.5^(t/8). Because the base is less than 1, the function decays.

Question 6

What is the half-life for the zombie population? Explain in terms of exponents. (To type an exponent, use the ^ key.)

Revolt · Accepted Answer

8 years. The factor 0.5^(t/8) equals 0.5 when the exponent t/8 is 1, which happens when t = 8.

Question 7

Abel is years older than Zöe.

Revolt · Accepted Answer

3

Question 8

Choose the equation that relates the balances in the accounts y years after Martin opened his account.

Revolt · Accepted Answer

M = 1.22C

Question 9

Which expression relates h, the number of half-lives, and y, the number of years?h = 2.6 + yh = 2.6 – yh = 2.6yh = y/2.6

Revolt · Accepted Answer

h = y/2.6

Rewriting Exponential Functions Answers

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