Need help with algebra question ASAP

Question

7 people in town have caught a virus. The number of people that are infected increases by 15% daily. How many days until 1000 people are infected ? Round to the nearest whole day.

Answer 1

Something that increases by a constant percentage over a time period is an exponential function. The standard form is:

A(t) = A₀·(1 + rate)^t

1. A(t) = Number of infected people at time t (in days)
2. A₀ = initial value = 7
3. rate = infection rate expressed as a decimal = 0.15
4. t = days

A(t) = 7·(1 + 0.15)t = 7·(1.15)^t

You are given A(t) = 1000 and asked to find t, the number of days needed to reach 1000.

1000 = 7·(1.15)^t

1000/7 = 1.15^t

To get the t out of the exponent, use logs. I'll use log base 10 which is written as just log. As the question states, round to the nearest whole day.

log(1000/7) = log(1.15^t)

Use the log property log(a^b) = b·log(a):

log(1000/7) = t·log(1.15)

log(1000/7)/log(1.15) = t

OK, we've used logs to solve for t. Now use the log (base 10) function on your calculator to get an answer, As the question states, round to the nearest whole day.

Answer 2

1000 = 7(1.15)^t

142.857 ≈ 1.15^t

ln 142.857 ≈ t ln 1.15

4.962 ≈ 0.140 t

35.503 ≈ t