A chain of retail computer stores opened 2 stores in its first year of operation. After 8 years of operation, the chain consisted of 206 stores. If the number of stores opening per year is increasing at an exponential rate, identify the continuous rate of growth. Round k to the nearest hundredth. *

0.66

Step-by-step explanation:

The exponential growth equation is expressed as;

S(t) = S0e^kt

S(t) is the number of stores after t years

S0 is the initial number of stores

If a chain of retail computer stores opened 2 stores in its first year of operation then at t = 1, S(t) = 2. Substitute into the equation;

2 = S0e^k(1)

2 = S0e^k .... 1

Also if after 8 years of operation, the chain consisted of 206 stores, this means at t = 8, S(t) = 206. Substitute into the equation;

206 = S0e^k(1)

206 = S0e^8k .... 2

Next is to calculate the value of k

Divide equation 2 by 1;

Hence the value of k to the nearest hundredth is 0.66

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