Forecasting with estimated AR model..conflict between EOC questions?

CFA Level II Quant
#1

Questions 17 and 8 in Reading 11 (Time Series Analysis) seem to conflict in their approach to solving.

In question 8, you plug in the change in (log sales) between t and t-1 which is just the difference of log sales between the periods…makes sense!

However in question 17, you plug in [(log sales(t-1) - log sales(t-2)] which in the answers, is log(1.01). presumable this number is because the question states “sales grew by 1 per cent last quarter.”

But I don’t get why it is log(1.01) not log(0.01)? Where did the 1 come from?

#2

log (sales (t-1)) - log(sales(t-2)) --> you need to understand a little bit of math for this

= log (sales (t-1) / sales(t-2))

Log of ratio of 2 numbers = difference of the logs of each of the numbers.

and since that growth was 1% -> that ratio sales(t-1) / sales(t-2) = 1.01

so finally it is log(1.01)