Question

give the percent increase or percent decrease for each equation.

1. $y = 50(2)^x$
2. $y = 1.25(0.95)^x$
3. $y = 0.9(0.8)^x$
4. $y = 3(3.4)^x$
5. $y = 10(0.855)^x$
6. $y = 30(10)^x$
7. $y = 0.5(1.23)^x$
8. $y = 1.3(0.005)^x$
9. $y = 2(1.3)^x$
10. $y = 1.5(0.45)^x$
11. $y = 0.5(0.3)^x$
12. $y = 1.3(4.075)^x$

Explanation:

Step1: Recall exponential form rule

Exponential growth/decay form: $y = a(b)^x$, where $b = 1 + r$ (growth, $r>0$) or $b = 1 - r$ (decay, $r<0$). $r$ is decimal rate, convert to % by $\times100$.

Step2: Solve #19: $y=50(2)^x$

$b=2=1+r \implies r=2-1=1$. Percent increase: $1\times100=100\%$

Step3: Solve #21: $y=1.25(0.95)^x$

$b=0.95=1-r \implies r=1-0.95=0.05$. Percent decrease: $0.05\times100=5\%$

Step4: Solve #22: $y=0.9(0.8)^x$

$b=0.8=1-r \implies r=1-0.8=0.2$. Percent decrease: $0.2\times100=20\%$

Step5: Solve #23: $y=3(3.4)^x$

$b=3.4=1+r \implies r=3.4-1=2.4$. Percent increase: $2.4\times100=240\%$

Step6: Solve #24: $y=10(0.855)^x$

$b=0.855=1-r \implies r=1-0.855=0.145$. Percent decrease: $0.145\times100=14.5\%$

Step7: Solve #25: $y=30(10)^x$

$b=10=1+r \implies r=10-1=9$. Percent increase: $9\times100=900\%$

Step8: Solve #26: $y=0.5(1.23)^x$

$b=1.23=1+r \implies r=1.23-1=0.23$. Percent increase: $0.23\times100=23\%$

Step9: Solve #27: $y=1.3(0.005)^x$

$b=0.005=1-r \implies r=1-0.005=0.995$. Percent decrease: $0.995\times100=99.5\%$

Step10: Solve #28: $y=2(1.3)^x$

$b=1.3=1+r \implies r=1.3-1=0.3$. Percent increase: $0.3\times100=30\%$

Step11: Solve #29: $y=1.5(0.45)^x$

$b=0.45=1-r \implies r=1-0.45=0.55$. Percent decrease: $0.55\times100=55\%$

Step12: Solve #30: $y=0.5(0.3)^x$

$b=0.3=1-r \implies r=1-0.3=0.7$. Percent decrease: $0.7\times100=70\%$

Step13: Solve #31: $y=1.3(4.075)^x$

$b=4.075=1+r \implies r=4.075-1=3.075$. Percent increase: $3.075\times100=307.5\%$

Answer:

1. 100% increase
2. 5% decrease
3. 20% decrease
4. 240% increase
5. 14.5% decrease
6. 900% increase
7. 23% increase
8. 99.5% decrease
9. 30% increase
10. 55% decrease
11. 70% decrease
12. 307.5% increase