Question

NEED MATH HELP!!!!
( with the 2 problems I missed)

Answer 1

`t=7.4years`

Explanation:

Let's clear t from the equation
`N=16.10^(0.15t)`. In order to clear t, we have to apply
`log_(10) (x)` in both side of the equations.

`log_(10)N=log_(10)(16.10)^(0.15t)`

By using properties of the logarithm

`log_(10) (a.b)}= log_(10)a+log_(10)b`

We obtain:

`log_(10)N=log_(10)(16)+log_(10) (10^(0.15t))`

Ordering using the logarithm property
`log_(10)a^(n) =nlog_(10)a` and
`log_(10) 10=1`

`log_(10)N=log_(10)(16)+0.15tlog_(10)10`

`log_(10)N=log_(10)(16)+0.15t`

Clearing t

`t=(log_(10)N-log_(10)(16))/(0.15)` using the logarith property
`log_(10)a-log_(10)b=log_(10)(a)/(b)`

we obtain:

`t=(log_(10)(N)/(16) )/(0.15)`

The number of Elm trees is N = 204

Solving

`t=(log_(10)(204)/(16) )/(0.15)\\t=(log_(10)12.75)/(0.15)=7.370`

Round to the nearest tenths place
`t=7.4years`