Hi so um can I receive help with this math homework question as soon as possible please

Question

Using an exponential model for the data, estimate when the population will exceed 100 million.

A.) The population will exceed 100 million in 2022.

B.) The population will exceed 100 million in 2011.

C.) The population will exceed 100 million in 2017.

D.) The population will exceed 100 million in 2008.

Answer 1

Let sstart count time from 2000. Then P(t) = 53·b^t. To get b we use in 2002 t = 2 and P(2) = 57;

We get equation: 57 = 53b², So, b = (57/53)^1/2 = 1.04.

Now we have population grow model: P(t) = 53(1.04)^t.

Let check how good it works for 2004: t = 4 P(4) = 53·(1.04)⁴ = 62

For 2006 t = 6 and P(6) = 53·(1.04)⁶ = 67

Now when 53·1.04^t >100; 1.04^t > 100/53; t > ln(100/53)/ln1.04 = 16.2 years;

So after 17 years in 2017 population became more 100 millions. answer is C.)

Answer 2

Need a formula.............