So I have the definition of the force of mortality as $\mu_t=-\frac{1}{l_x}\frac{d l_x}{dx}$ and I am given two different forces of mortality, one for females as $\mu_x^f=0.05(1.2)^x$ and the other for males as $\mu_x^m=0.07(1.2)^x$.

I am then asked to calculate an expression for $l_x$. So I am assuming that I am to assume that there is an equal distribution of females and males.

Do I now want to proceed calculating $l_x$ as follows?

$$l_x=l_x^f+l_x^m=l_0^f\exp\left (\int_0^x \mu_t^f dt\right )+l_o^m\exp\left ( \int_0^x\mu_t^mdt\right )$$

Thanks for any help

So I have the definition of the force of mortality as $\mu_x=-\frac{1}{l_x}\frac{d l_x}{dx}$ and I am given two different forces of mortality, one for females as $\mu_x^f=0.05(1.2)^x$ and the other for males as $\mu_x^m=0.07(1.2)^x$.

I am then asked to calculate an expression for $l_x$. So I am assuming that I am to assume that there is an equal distribution of females and males.

Do I now want to proceed calculating $l_x$ as follows?

$$l_x=l_x^f+l_x^m=l_0^f\exp\left (\int_0^x \mu_t^f dt\right )+l_o^m\exp\left ( \int_0^x\mu_t^mdt\right )$$