Suppose I run a poisson regression with yearly death count as outcome:

$\log \mu_{t}=a + \beta_{ti} \kappa_{ti} + offset$

$\mu_{t}$ refers to the number of death at time $t$; $a$ refers to intercept; $\kappa_t$ refers to age-group $i$ at time $t$. Noted that I have stratified the age into several groups, i.e. 0-4;5-9;10-14...etc

My question is that: Can I claim that the mortality rate of age group $i$ at time $t$ is $\beta_{ti}$?

Suppose I run a poisson regression with yearly death count as outcome:

$\log \mu_{t}=a + \beta_{ti} \kappa_{ti} + offset$

$\mu_{t}$ refers to the number of death at time $t$; $a$ refers to intercept; $\kappa_t$ refers to age-group $i$ at time $t$. Noted that I have stratified the age into several groups, i.e. 0-4;5-9;10-14...etc

My question is that: Can I claim that the mortality rate of age group $i$ at time $t$ is $exp(\beta_{ti})$?