Question

i need help with my homework PLEASE CHECK WORK WHEN DONENUMBER 10 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

Answer: B

`(log_(2)(4.72))/(0.32)`

Step-by-step explanation:

Step 1. The expression that we have is:

`P(t)=18,785\cdot2^(0.32t)`

This represents the population P after t years.

Step 2. We need to find the expression that represents the amount of time, t, in years, for the population to be 88,740:

`P(t)=88,740`

Step 3. Substituting this value of P(t) into the given equation:

`88,740=18,785\cdot2^(0.32t)`

Step 4. To solve for t, first, we divide both sides by 18,785:

`(88,740)/(18,785)=2^(0.32t)`

The result of the division is:

`4.72=2^(0.32t)`

Step 5. Then, to continue solving for x, we apply the logarithm base two to both sides:

`log_2(4.72)=log_2(2^(0.32t))`

We simplify applying this property of logarithms:

`log_2(a^x)=x\cdot log_2(a)`

The result is:

`log_2(4.72)=0.32t\cdot log_2(2^)`

And since:

`log_2(2^)=1`

The expression now is:

`log_2(4.72)=0.32t`

Step 6. Dividing both sides by 0.32 to solve for t:

`(log_2(4.72))/(0.32)=t`

This expression is shown in option B:

`(log_(2)(4.72))/(0.32)`

Answer: B

`(log_(2)(4.72))/(0.32)`