Question

suppose the price index was 105 in 2017, 126 in 2018, and the inflation rate was lower between 2018 and 2019 than it was between 2017 and 2018. this means that_. the price index in 2019 was lower than 126.0. the price index in 2019 was lower than 147.0. the price index in 2019 was lower than 151.2. the inflation rate between 2018 and 2019 was lower than 1.2 percent.

Explanation:

Step1: Recall inflation - rate formula

The inflation rate formula is $\text{Inflation Rate}=\frac{\text{Price Index}_{t}-\text{Price Index}_{t - 1}}{\text{Price Index}_{t - 1}}\times100\%$. The price index in 2017 is $P_{2017}=105$, in 2018 is $P_{2018}=126$, and assume in 2019 is $P_{2019}$.

Step2: Calculate inflation rate between 2017 - 2018

$\text{Inflation Rate}_{2017 - 2018}=\frac{P_{2018}-P_{2017}}{P_{2017}}\times100\%=\frac{126 - 105}{105}\times100\%=\frac{21}{105}\times100\% = 20\%$.

Step3: Analyze given conditions

We know that the inflation rate between 2018 and 2019 is lower than it was between 2017 and 2018 (20%) and lower than 1.2%. Let's check the price - index conditions. If the inflation rate $\text{Inflation Rate}_{2018 - 2019}=\frac{P_{2019}-P_{2018}}{P_{2018}}\times100\%<1.2\%$. Substituting $P_{2018} = 126$, we get $\frac{P_{2019}-126}{126}\times100\%<1.2\%$. Then $P_{2019}-126<\frac{1.2}{100}\times126=1.512$, so $P_{2019}<126 + 1.512=127.512$.

Answer:

The price index in 2019 was lower than 126.0.