Question

(1 point) The length of an insect (L, in mm) is a function of the temperature during development (T , measured in ∘C according to L(T)=8+T10 ) . The volume of the insect (V , in cubic mm) is a function of the length according to V(L)=7L3 . The mass (M in milligrams) depends on volume according to M(V)=1.1V . Find mass as a function of temperature. M(T)= How much would an insect weigh that developed at 22∘C?

Answer 1

`M(T)=1.1(7(8+T^(10))^(3))` and
`M(T)=1.1(7(8+22^(10))^(3))=1.44\time10^(41)`

Explanation:

We have the next set of functions:

`L(T)=8+T^(10)`

`V(L)=7L^(3)`

`M(V)=1.1V`

We want to know M(T) then:

`M(V)=1.1V` but we know that
`V(L)=7L^(3)`:

`M(L)=1.1(7L^(3))` and we know that
`L(T)=8+T^(10)`

`M(T)=1.1(7(8+T^(10))^(3))`

Finally using the value of 22º we have

`M(T)=1.1(7(8+22^(10))^(3))=1.44\time10^(41)`