Question

1. Solve the equation to find the value of x. Show all of your steps.
log2 (5x - 4) = 4
A. 6/5**
B. 4
C. 8
D. 256/5

2. The population of a town is modeled by the equation P=3485e^0.12t, where “P” represents the population as of the year 2000.
*According to the model, what will the population of the town be in 2010?
*In approximately what year will the population reach 50,000 people?
*Must answer and show appropriate work for both questions here.
A. Part A: 11,571 people in 2010
Part B: approx. 22 years**

B. Part A: 38,416 people in 2010
Part B: approx. 13 years

C. Part A: 11,571 people in 2010;
Part B: approx. 13 years

D. Part A: 38,416 people in 2010;
Part B: approx. 22 years

Can someone please help me asap? I'm so lost

Answer 1

log2 (5x - 4) = 4
5x-4 = 2^4
5x = 20
x = 4
------------------------
P=3485e^0.12t
in 2010, t=10, so
P=3485e^1.2 = 11571

3485e^0.12t = 50000
e^0.12t = 14.347
0.12t = ln14.347 = 2.663
t = 22.196
so A is correct

Answer 2

D. Part A: 38,416 people in 2010; Part B: approx. 22 years