7 fill in the blank 1 point\nlodine - 131 decreases 50% every day. about how much is left from a 50 - gram…

Question 7

Answer:

0.01

Explanation:

Step1: Identify the decay formula

The formula for exponential decay is $A = A_0(1 - r)^t$, where $A_0$ is the initial amount, $r$ is the rate of decay, and $t$ is the time. Here, $A_0=50$, $r = 0.5$, and $t = 12$.

Step2: Substitute values into the formula

$A=50\times(1 - 0.5)^{12}=50\times0.5^{12}$.

Step3: Calculate the result

$0.5^{12}=\frac{1}{2^{12}}=\frac{1}{4096}$, and $50\times\frac{1}{4096}\approx0.0122$. Rounding to the nearest hundred - th gives 0.01.

Question 8

Answer:

1408

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is $A=P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. Here, $P = 1200$, $r=0.0325$, and $t = 5$.

Step2: Substitute values into the formula

$A = 1200\times(1+0.0325)^{5}$.

Step3: Calculate $(1 + 0.0325)^{5}$

$(1 + 0.0325)^{5}=1.0325^{5}\approx1.1733$.

Step4: Calculate the total amount

$A=1200\times1.1733 = 1407.96\approx1408$.

Question 9

Answer:

291

Explanation:

Step1: Identify the growth formula

The formula for exponential growth is $A = A_0(1 + r)^t$, where $A_0$ is the initial amount, $r$ is the rate of growth, and $t$ is the time. Here, $A_0 = 240$, $r=0.05$, and $t = 4$.

Step2: Substitute values into the formula

$A=240\times(1 + 0.05)^{4}$.

Step3: Calculate $(1 + 0.05)^{4}$

$(1 + 0.05)^{4}=1.05^{4}=1.05\times1.05\times1.05\times1.05=1.21550625$.

Step4: Calculate the number of members

$A=240\times1.21550625 = 291.7215\approx291$.